Like all flora & fauna, they have to come up eventually. I have picked morels with some snow on the ground, but not when we have an inch or more total snowfall. I had limited luck last weekend and this cooler weather may slow them down, but it won't wipe them out. The moisture will actually helps us to have bigger & densely formed yellows with an increased heaviness per morel. Remember Grammie, they are known as 'spongies'. Get out friday and you might be surprised!
Good luck & Happy Hunting!