Growing grass in shade is often possible, but can be difficult. The drainage may also effect the ability to grow grass. Is there a way you trim you trees up so that the lawn has at least some sun?

There are lots of ivy's that I'm sure you could grow there in the shade, but it could be an eyesore. Honestly, if I were you, I would be tempted to try bluegrass or fescue sod. That way it doesn't have the whole growing process to go through. All it needs to do is grow roots, which shouldn't be a huge deal. It will thin out, but shouldn't die out.

If you do try seed, but down only about 4-5 lbs. per 1000 sq. ft. It will have to be babied as in not too much water etc. I have seen quite a few yards that are very shaded that do just fine with grass, so there's a chance you could do it. But again, I think the best is a tree trimming - if possible.

The time to seed is in the fall. If you were thinking of waiting until next spring, be glad you asked with plenty of time to get reoriented. Seeding in the spring is going to sprout all the summer weeds (like crabgrass) along with your grass seed. Seeding in the fall gives the new grass plenty of time to harden off the roots so they can withstand next summer's heat. Sod will work any time. The roots are already established. Sod is a lot more expensive, but gives instant results.

Fescue is the best grass in the north for shade. Some varieties are better than others. I can't help you with which is which. Kentucky bluegrass is a full-sun type of grass. Doesn't sound like that will work for you.

If you have too much shade for fescue, then there are some ground covers that look like grass. Dwarf monkey grass, aka mondo grass, might work. Not sure how it takes to being snowed upon, but it works fine without snow. Unfortunately it takes eons to spread. I started with a 1 foot patch in my lawn 20 years ago. I left it alone knowing it spread slowly. Now it covers about 10 square feet.

To expand on David's remarks about fescue, you probably want fine fescues rather than tall fescues. I've never used it, but I've read good reviews of the Bonny Dunes mix. It's available at a number of online retailers.