I don't think anything in Park City will be open. Snowbird should still be spinning the wheels, though it might be down to limited operations. Right now they are a seven day a week operation.
Arapahoe Basin is the loan gig in Colorado now. They are open until the first weekend of June. Snow can happen through that month. It's also off season, so you should be able to find cheap lodging in Summit county. The Silverthorne, Keystone, Dillon area is ideal.
Mammoth should also still be running.
Mt Hood (Meadows I believe) pretty much runs year round except for a few weeks in September. You can always go there.