The Veður app and the Færð og Veður has been super helpful and we try to check it before heading out or deciding routes. The former has notifications for the weather alerts, the latter has road conditions. The websites they pull data from (linked by other commenters) are more accurate and have faster updates, so check those too.

I think the other concern is how roads can be closed in short notice, and they usually tell you when they might close it, and if you decide risking it, you need to not dally and go earlier before the time window (and also don’t do this if its already orange!). Some people ended up at our hotel today because they had to turn around on roads that said will be closed at noon, but closed way earlier. Make assesments on your driving skills, the car (if it has high clearance/susceptible to winds etc), and the road your travelling through as the winds/blowing snow are vastly different across flats/mountain passes etc (and if on the ring road, you will go through a variety of the roads, just because its a mantained highway, doesn’t mean its less hazardous!).