I've had the same experience as Chelle. Bulbs here freeze and thaw, and they grow fine. Are you concerned about the pot itself freezing and breaking? I've had that happen to some clay pots, ugh. I've switched to plastic pots so I don't have to drag them in or cover them. If the pot doesn't drain well, and your weather is above freezing, THEN you might have an issue with rot. Use good soil and make sure the pot has holes in the bottom.
Our winters are so dry, most years, that I have to water plants. Yep, that means take out the hoses, water, drain the hoses, put them away. Evergreens particularly need that water. LAst winter, we had lots of rain and snow, and the bulbs came through without issues.
I had one bag of tulips that I purchased on clearance in December that I didnt' get planted. It sat outside in the rain and snow. Come spring, there were green shoots coming out of that bag. A couple of the bulbs were rotted, and boy did they stink...but the rest actually grew and bloomed once I finally got them into soil! Just like Chelle, though, I have lost bulbs by forgetting them in the garage over the winter where they dried out.
What matters most, though, is What Kind of bulbs are you talking about? That will make a huge difference.
