No, I think it's way too soon, unless you just want to feed the birds, lol. I'd wait until the latter part of March.

it is too soon. march/april depending on the weather in your area. clearly avoid frozen /water logged soil and prepare the ground thoroughly before you sow. as for which seed it will depend on the type of grass you want. you can get seed mixes for shady areas, hard working / play areas and top quality lawn mix. so decide what you want to use the grass for then buy the appropriate mix.

You also don't have to rely entirely on the hype of the bag label. There are three basic types of turf grass: clumping, including perennial ryegrass, tall fescue, and Chewings fescue; stoloniferous, including creeping fescue, bent grass, and roughstalk bluegrass; and rhizomatous, primarily "Kentucky" bluegrass, among the hardy turf grasses.
Clumping grasses include some of the deepest rooted and most heat tolerant species, but they need regular--about every 2-3 years--re-seeding to keep them from becoming polka-dotted. If traffic or other stress produces trails or bare patches in the turf, the only remedy is again re-seeding, since the spread of the clumps is limited.
Stoloniferous species are slightly more wear resistant, since the stolons can weave a fairly dense mat of sod, but if bare patches appear, they only heal by growth from the edges, which can take some time, unless also re-seeded.
Rhizomatous species may show bare patches, but if the damage only affects the surface, new growth will appear from the rhizomes below, rapidly repairing the turf. Deeper damage heals the same way as in stoloniferous species, and can take just as long.

I always think it's best to wait for 10C before sowing grass seed or else the birds just get it before it gets a chance to germinate. :)

The soil this time of year is not at all workable. Take a few more months to relax.

If you have borders of beds avoid anything that creeps sideways.....