pianotuna wrote:
Gdetrailer,
Does it retain it's "memory" if the power goes off?
Yes.
Uses a Lithium "CR" button style battery which should be pretty good even in extreme cold weather.
Example is a popular CR2032
HERE operating temp is -30C to +60C (note Celsius) and has a self discharge rate of about 1% per yr and typically you can expect 5 to 10 yrs from them.
Otherwise, what would be the point of a timer that looses not only the time but the programming..
You can also opt for the simpler and cheaper "mechanical" versions that use a adjustable "pin" to trip on/off, those typically give you 30 minute increments and are "24hr" type which means the program repeats every 24 hrs.

Found
HERE for about $8
Granted, the time will stop when you lose power, no big deal when it comes to charging a battery and you can leave it pickup anytime the power comes back on or adjust it.
Dirt cheap, simple and reliable.
My local Ham radio clubs used the simple timer method for 20 some yrs to maintain backup power (old car battery) for the clubs emergency communications shack.. Now days they use newer tech but idea is still the same.
As a note, you want one that is rated for appliances which uses relays or mechanical switches. Ones not rated for appliances can and often use solid state Triac devices to do the switching which may not work well with your converter or power supply.