We had an artesian stock tank off our spring here and with running spring water it never froze, and the place I lived before, I busted ice and carried. I've heard too many stories about fried horses. A ground fault interrupter is essential. I have run chicken water heaters off heavy-duty made for outside use extension cords, but would worry about the integrity of the wires with large livestock cribbing at, stepping on or even brushing against the wires.

What we do have installed here outside are bayonet outside hydrants. They are freeze proof and you just trench to where you want them below the frost line, mount them to the water line and near your stock tank. Might sound like a PIA, but not that hard if you have access to or can rent a trencher in which to lay that line. Not that expensive (cheaper than a horse) and a good day or two work and it's done and you're good to go. And it's safe.

I have four of these mounted for irrigation work. If you have a water supply halfway handy they make life easy. You can buy one of them somewhere in the $100 to $200 dollar range, depending on how heavy-duty you need them. The cost of the pipe to run from your main source and a little trenching work.

Here is a link that might be useful: freeze proof outdoor hydrants

Extension cord would work if you can keep it up out of the way check the wattage of the heater and buy the best cord you can afford to match that some might come with a built in ground fault

Another idea is an insulated solar stock tank

Here is a link that might be useful: stock tank plans

I've only used the floating tank heaters. With horses, you have to cover part of the tank and have the heater under the covered part, so they can't reach it.

If you have an exterior grade extension cord, it shouldn't matter whether it is lying on the ground or not. Do not bury it.

If you want to bury the wire, get exterior rated coated electrical wire, with each interior wore also wrapped. Don't mess with it unless you are a qualified electrician, or hire an electrician to do the wiring. It must be installed correctly and grounded correctly.

The cord where the horses can reach it, should be inside pipe so the horses can't get their teeth on it.

For any appliance that produces heat, you need a very heavy grade of extension cord. The cheap ones will overheat the cord and probably burn out your heater. Good heavy extension cords are quite expensive, in the neighborhood of $1 per foot. Do not use the nice cheap orange ones that cost $8 for a 100 foot cord. They are not heavy enough.

I would run an underground line in conduit to your place of need and install an exterior box with a GFCI outlet. We use a heated bucket here in the winter and it gets into the -40s with little trouble. We still have to carry water in winter because a heated line all the way to the barn is too expensive to run. The ground freezes 10 to 12 feet down so any line with water in it will freeze unless you insulate and heat it. Anyway, I don't like semi-permanent extension cords laying on the surface. If you decide to use an extension cord, elevate it to keep it out of trouble.

Put in a Mirafont water tank. It doesn't require electricity and as long as you have 4-5 animals drinking out of it regularly is shouldn't freeze.

Guess I do it the hillbilly way. I run a 16ga orange extension cord from the shed to the trough. It just lays on the ground and gets covered by several feet of snow. Most years I don't use cords long enough so I plug two of them together. If I am feeling really "safe" I'll run electrical tape around the seam where the two cords are plugged into one another. I've been doing it this way for years with heat lamps, heated bases for poultry waterers, and for floating stock tank heaters.

I would go with Donnalaska's suggestion of putting in wire and a new outlet!

You certainly have enough good weather time left to trench in a conduit and HEAVY guage wire, get the outlet installed.

You could call an electrician, ask how deep, what gauge wire, probably at least 12ga, and size of conduit. Then you could do the trench to depth specified, have the conduit, wire, outlet and GFCI for him to put in place. Having done the 'dirty work' yourself, everything should fall into place quickly for the install. He won't need much time, so his charge would be cheaper.

Does your garage have a circut for that outlet? Water heaters draw a LOT of power. Uninsulated tank will draw even MORE power with having to run the heater more often. You REALLY do not want to have long extension cords, small gauge 14-16, powering the heater. Just looking for trouble. And the chance of DRIVING OVER the wire is just careless waiting to cause problems!! Insulation of ANY WIRE is not designed to stand up to tire traffic!!! Can cut right thru to wires. Over powered, long, light extension cords get HOT, insulation may melt and wires touching can start fires. Ask ANY fireman! Common cause of fires for winter.

Buried wire in conduit is about the safest, won't get in your way working around the farm. Not going to cut or break it by hitting it.

You might want to consider making an insulated box for your tank. Wood frame, plywood sheathing, styrofoam sheets inside, with the half cover over top to keep in more heat. Our horses come inside at night, so I cover the open side, just run my heater at night on the 'cheap night rates' instead of all the time. I have cut tank expenses a bunch, on that system.

I am not a fan of Rubbermaid tanks and heaters, since we burned up a tank. So be aware they CAN catch fire. Lucky us, tank was way outside the barn, neighbor saw the flames, came and put them out. He said they were 4ft high!! Now we use only metal tanks with sunken heaters. With the right wire to GFCI outlet, no extension cords, heaters last a long time of use.

There are 5 photos of our box on the link. Tank backs up to a fence, my horses don't bother the cord coming out the back side. Half top is screwed down protecting the exit of cord. Have not had a problem with my horses. However running the cord thru a piece of pipe is a very good idea, successful for many. PVC works fine as protection for cord usually, depends on horse boredom and determination to wreck things. The pink styrofoam is the cover that I put on and take off daily.

Here is a link that might be useful: Insulated box for water tank

The water tanks by
rainwater filters are the best and they really work great.

I've been using the regular old orange heavy duty electrical cords for the past 20 years. I tie them end to end and wrap them in a plastic bag to protect the plugs. Have used them to stretch 200 to 300 ft. with no problem. Just don't put them where livestock would chew on them or where you might accidentally mow over them. I use rubbermaid tanks (100gal) with bowtie heaters in the bottom. I've found that horses like to toss the floating heaters.