Yeast in the cold

I made a 5 gallon batch last night....3 gallons of water and about 2.5 in the boil. I had a good starter to dump into the brew after the boil was over. My question is about yeast in cold temps. I boiled the 3 gallons of plain water the night before and stuck it in my deep freeze. It froze pretty well, not all the way solid, but the 2 gallons of hot boil didnt end up melting it quite all the way. So it was fairly cold, but I needed to get to bed so I dumped my starter in because I didnt want to leave it sit overnight without yeast in there. The fermenting is going fine so far as I can tell....what I was wondering, does cold kill yeast or just make it dormant. And also, if I hadn't put the starter in til morning, would the cold make it okay because other bacteria wouldnt be able to do much in there either. (next time im going to balance the frozen to boiled ratio a little better anyways)

If I do all DME I usually place 4 gals of water in the freezer for 4-5 hours prio to brewing.

If I do some grain I only use 3 gals because of needing 1 gal to sparge my grains with.

I've never had any problems doing this in this manner.

I would not have like to leave a wort without some yeast in it overnight.

As long as you stirred the two together (no hot or cold spots) then your brew should be fine.

Yeast are fairly tough, you probably killed some of them, but not too many. Most brewing yeasts can't form spores and there really wasn't time. Bacteria do not do well in the cold, but you were better off pitching when you did.