My two picks for your needs, perfect for your acreage:
John Deere 2000 series sub-compact 4x4, belly mower and snow blade available:
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Kubota BX-series sub-compact 4x4, belly mower and snow blade available:
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You'll also be cleaning out the stalls and barn.

You definitely want a 4wd sub cut like a BX Kubota or JD 2505 (actually being replaced as we speak with a new model) with an FEL.

The best way to move a lot of snow fast is with a blower and the snow is really out of the way. On a sub cut it can be either front or rear mounted. Moving snow with an FEL is fun at first then it get REAL tedious. Using a blade, storm after storm, the area gets narrower and sooner or later you'll be out there with the FEL moving the snow again.

Mowing can be done with a MMM or for less money with a rear mounted axial as pictures above.

You could get away with a JD X7xx series but by the time you equip it as you need you'll spend more than a sub cut and have a less flexible tractor.

Lawn or garden tractor is small for what you'll need.

Check with you horse loving neighbors and ask what they have/use and get recommendations for the local tractor dealers. A good local dealer should make the decision on what color tractor easier to make.

Every property brings its own special needs to the table and all too often, there is no such thing as one machine that will do it all.

A fifteen acre horse farm that has horses will also have enclosed pasture areas for daily turnout. Horses are gourmet-type eaters compared to other livestock. The love to nibble on tender grass but the won't touch weeds. You are going to need a true CUT with a seven or eight foot three-point finishing mower on it or you are going to spend way too much of your time cutting grass.

You will also need a regular lawn tractor to take care of areas close to the house, stable, outbuildings, driveway, around trees, flower beds and to open up the pasture for the big mower by making a pass next to the expensive fencing. If you clobber the fence with the big tractor, you may end up with two repair bills. One for the fence and another for the damage to the mower or tractor.

You can either look after the fence lines with a string trimmer or you can spray Round-up around the posts and directly below the fence boards twice a year to eliminate the grass and weeds. I also suggest that you install an electric fencing system on your fencing to protect it and your horses.

It's easy for us to sit back and make suggestions but this also comes down to your budget. In my opinion, you are better off with a low hour used CUT than you are with a brand new 700 series Deere or equivalent. Time on a horse farm is a precious commodity because there is always something in need of repair or upgrade. Horses require a lot of daily attention and there are only so many hours available. So, choose wisely or you will quickly regret making the wrong choice.

I've got a similar property, but no woods. I have a New Holland TC30 with a loader and a finish mower. My other tractor is a JD X500. I really with I would have bought a sub compact sometimes, but when it comes to pulling a hay rack etc the extra weight of the TC30 helps. The garden tractor does most of the snow with the loader doing the heavy stuff.

I would stay away from a lawn tractor. You may be able to get by with a Garden tractor for a few years, but as other have indicated you'll probably eventually want a sub-compact utility tractor (sub-CUT) or a CUT.

If you start out with a good Garden tractor it will be worth keeping even should you later get a CUT.

You don't say where you are, but a Garden Tractor with a snow blade is useful for snow. On the better tractors the blade can be used to move dirt as well. A tractor mounter snow blower is good as well, but very expensive.

Here is a link that might be useful: Some good info on tractors