If you already had a place picked that's in the north, make sure you settle in as early as a month or two before it's winter season starts.
Do not ever neglect snow tires. If you're tight on money, getting even 2 sets of tires for wintry conditions is better than none. But 4 is still recommended and no, All-Seasons are terrible for winters regardless of brand. They just aren't designed for winter conditions, they're designed mostly for Spring/Summer/Fall.
Buy winter emergency sets for your vehicle. Buy one for the glove compartment, the ones where they actually have emergency power banks in them. Buy another for general use, especially ones equipped with a piece together shovel.
Just going to throw out that electric heaters are the most expensive/least efficient way to heat electrically.
If you’re in the US, you can get a partial credit for improving windows, doors, and insulation (always the best first step).
You or your landlord can also get up to a $3000 credit toward a central heat pump system, which gives 3-4x the delivered heat for a given amount of electricity.