Well you can always try and see how being car-free goes now that you have a chance, and buy another vehicle later if it doesn't work out for you. Is your commute doable by public transit? If you have the backup of transit for your winter commute, you can probably work out errands and trips. If trips are infrequent, renting a car for the weekend is often cheaper than having insurance on a car year round. You can get free credit cards that cover the CDW insurance. (this is what I do not having a car in case I want to rent one although I rarely do)

For errands, having a bike trailer comes in handy. In winter, if you can't find a way to deal with the cold (asthma of course makes it much more challenging), are there car-sharing programs you can join where you live? They usually are quite ideal for errands and again cheaper than insuring a car you own if you're going to use the car infrequently.

It doesn't have to be all or nothing - you can be car-lite rather than car-free by car sharing for the times when you need a car. You'll probably end up driving a lot less than if you owned a car because you'll think about each trip, do I really need a car for this or no?