You won't need the snow tyres. It hasn't snowed in awhile so you won't even need chains. My group arrived around 11am last Sunday and managed to get into the first lot, though it was much busier than at 9am which is when we normally arrive (leaving around 6:30 but we make a few stops to pick people up).
Stevens on the weekend has been packed ever since ski/snowboard school started. My friends who could do the backside escaped there but the rest of us stuck to Brooks and Skyline, which were both far less crowded than Hogsback. Last Sunday you could almost ride straight onto the Brooks chairlift while Hogsback was chockers.