The issue isn't "I don't want to be cold." The problem is when it's below 20F/-7C, you need to wait long enough for the coolant to warm enough to evaporate the moisture in the defrost vents and the inside of the windshield. Otherwise the inside of the windshield frosts over and you can't see well enough to drive safely. And the colder it gets, the longer it takes.
Do you need remote start? Nope. I don't have it on my vehicles. But you will need to wait long enough to keep the windshield defrosted.
It's a nice thought, but it has so many modifiers it's pretty much worthless. Everything from road conditions, to time of day or night, to the size and weight and type of vehicle you are driving, to how old you are affects stopping distance and the interval you should be leaving.
Remember children - Driving should never be "relaxing." It's real work and demands your total concentration to protect yourself and everyone around you. So put the phone down and even turn off the radio. Put your head on a swivel like a fighter pilot. And have an escape plan for every inch you drive.