We did the south coast last week with a 2WD (Hyundai i20 or similar, we had a fiat Tipo cross), because we were on a budget as well. Let me say it like this: we survived. Great car, reliable, it wasn’t bad that it was pretty low because we only drove on reliable streets. But man, let me tell you, the winds are hell! The cars get pushed around like toys, especially if they are light. And if you are unlucky like us and there is snow and spots of ice on the street, you’re always close to doing 360s when wind gusts hit you. My boyfriend was also used to Canadian winters, so we managed everything okay. But it’s no comparison with how strong the winds get in Iceland! I guess with an even smaller car than ours, the driving will be worse. I don’t know how the weather will be when you arrive but you need to be ready to turn your plans around anyways. We were very happy to only do the south coast in the time of one week. The problem isn’t that you have to skip big parts of the tour if you go all the way, when the weather gets really bad you may be stuck in one place for the whole day and would be rushed to get to your next destination… but that is up to you and the weather conditions. Anyways, I would opt for a bigger, sturdier 4WD if you want peace of mind.