So, as I live in NJ where the temp is now 25-50F, would it do the player any harm if I were to listen to the AUX until the interior of the car warmed up?

Yes and no...

I have started my empeg quite a few times at temperatures below zero F, and it did start up and run. The limit on my player seemed to be about -15 degrees F, where it wouldn't start until I laid it on the floor under the heater outlet for about 10 minutes. So from that point of view, sure, no problems.

However... my hard drive did fail (bad sectors/head crash) after about three years of this abuse, and while I can't prove it, I suspect those cold starts did contribute to the problem. Although... it did get pretty rough usage (bumps/impacts) when I used it on my bicycle .

tanstaafl.