I'm still amazed that you can buy remote starters in MA. Their very use goes against 2 different state laws. (1 for leaving a running vehicle unattended and another one for idling over 5 minutes.) Not that the laws are enforced in MA outside of fleets operating at Logan, but... (That, and the OP was from the Land of the Free NH)
anyhow, anything is possible. but you'd have to leave a registered keyfob inside the car. (so, there goes your rolling-ID engine immobilizer). If you have SE&SS/SKS, you cannot leave a smart fob inside, as then you can never lock your car doors except with the little metallic key (same goes if you leave the keyfob in the dash slot).
The Prius warms up fast enough in the winter. Plus, it's better on the engine and better for MPG/emissions (on any car) to warm it up under load (driving it) as compared to idling it, and it'll warm up faster when driven, too.