Re: External HD not recognized, not spinning
bummer about the enclosure: i had my feeling on that. to answer your question on data loss, no, it won't affect anything. it's not like you're going from freezing to out in the hot sun. freezing it for a few hours should work and if it doesn't, then the drive is truly dead. sure, the drive will get hot, as any drive will, during use, and that will dry up any condensation fast, so no issues.
The other thing you could do, although too time consuming and a huge hassle (if it can be done at all), is take it apart and put drive assembly with a working motor...if possible. this is a hassle and you may not even be able to do it. i wouldn't risk it. this is one of the main things data retrieval houses do, and why they charge so much!
when i did the freezer trick, it was in for about 4 hours or so. no bag, just the hard drive itself. once removed, i connected it and the OS saw it right away. i was always able to pull data off it. we tried it on a drive here at work, no go. the drive was truly dead. if you needed to do it a couple times, i would wait maybe a day between attempts. the reason for this... to make sure any condensation (IF there is any, is dried.) you don't want to FREEZE the unit up with ice. if you freeze it when it's dry, it will cause the metal to contract, which does something to the motor, and will enable to spin...hopefully.