I cant see why not. I cant claim to be a weather expert but I would imagine it would be extremely scenic at that time of year.

There is an organized Crossing of the Lakes (El cruce de lagos) which does not require any car rental and ends up in Puerto Montt.

I found this site :

http://www.ladatco.com/Lake-BRC.HTM

Puerto Montt would be a good place to rent a car and head up to Pucon, Puerto Varas etc.

By the way 2 other spots which plenty of people overlook are San Pedro de Atacama in the north of Chile - the driest place on earth outside of Antarctica and Perito Moreno Glacier near El Calafate in Southern Argentina. You need to fly from Santiago to Calama, the world's driest town, to get to San Pedro. If the lunar landings were fake this is where they would have filmed it! Perito Moreno is an advancing glacier which can be observed from a viewing platform a few hundred metres away. It is possible to fly from San Carlos de Bariloche to El Calafate on Aerolineas. Renting a car is a decent option in any of these places. You certainly wont encounter the Formula 1 style racing that you may encounter in the larger cities.