I agree with the mods suggested for the older carb bikes, you don't have to drop a lot of money, just a little shop time and check out other bikes.
Some of the older 03 and up mx bikes work great for snow bikes, check for reviews, but some of the earlier Yam had nasty abrupt power bands, hard to race, but perfect for snow bike. If its a four stroke 450, starts easy and doesn't smoke, don't touch the valves or pistons, you're ok. Make sure it holds anti freeze and water pump works. Change oil and filter, ride an hour and dump oil, if its clean its a runner most likely.
Try and find an MX bike someone bought for trails, they are rarely ridden hard or ridden at all.....bad choice for trailer rider but good sno bike donor. Often dinged but seldom is the engine wore out.