Got a 1000 dollar discount on asphalt driveway for winter promotion but they want to start this week. Is that okay weather wise?

I've been getting quotes for an asphalt driveway and most came in around 4500-5000 and they all said they can start in April since the ground needs to thaw. I got another quote yesterday and they said it's a 4700 job but will give the winter discount of 1000 so 3700 final price. However he said they would start asap.

I'm in Toronto and we've had a streak of warm weather but it looks to be going back to near zero temps soon. Is it fine to do the excavation and gravel part of the driveway and lay the asphalt mid April or is it that going to potentially cause problems down the road since the ground wasn't fully thawed?