You can’t switch from ac to heat for $200. They are completely separate systems that operate on completely different principles. It’s not like a heat pump (AC system for a house that is cooling outside air and heating inside air). Maybe their talking about attempting to reverse the AC system as a hack. This would not be good. Like at all. Wouldn’t damage the “engine” but probably mess up the ac system if it worked at all.

Automotive heating systems work by using engine coolant to heat air passing through a heat exchanger (think a small radiator) buried in the dash to heat the air for the cabin.

Ac uses two separate heat exchangers (the evaporator core in the dash and the condenser in front of radiator in the front of the car). Without getting too far into the weeds, it uses the state change of the refrigerant and the resulting pressure change to create the temperature difference. The evaporator gets cold and the condenser gets hot.

What’s wrong with the heater core? Is it leaking? Clogged? If it’s leaking, it needs to be bypassed until it get repaired. If you guys are at all handy, it can be changed yourselves, although usually requiring removing most or all of the dash from inside the car. I doubt the core itself is all that expensive, it’s the labor that’s most of the bill. Consult the repair manual and or diy videos if you go that route. The route I would take.

In terms of financing or leasing - it’s a trade off. Leasing is essentially renting the vehicle with mileage limits etc.
Financing, you own the vehicle once the loan is paid. If you care about having a “new” car and expect to want to get a “new” car after the lease is up in 3 years, leasing is probably a good fit for you.

If you want a car for longer than that, I’d recommend buying a vehicle. Since you mentioned winters, I’m assuming salt and rust in your area. Look for a 5-7yr old vehicle with 60-75k miles. It should easily last for a 6yr loan term without major expenses/repair so long as it’s maintained properly and is a make/model known for reliability. Should be able to find something that’ll meet your needs with around a 300 payment. Especially with a trade and potential down payment. Personally I’ve never put money down, instead I just purchase vehicles where I could afford to finance the entire purchase with excellent credit. I’d save the cash if I were you. Keep it in your emergency fund to not set back your long term goals.