We have driven the route - but not in April, I'm afraid, so I don't know how much snow would be around or how well the road is cleared. It's a spectacular route which will have you stopping to admire the view every few minutes. You would be able to find more information and someone to answer your question on here:

http://www.fodors.com/forums/threadselect.jsp?fid=29

The road is open all year round but it's right at the end of the winter season so it's hard to say what driving will be like, it could be springlike or there could be a lot of snow around, If there are heavy snowfalls the road is often closed for up to 3 days. There is a possibility of black ice on the roads in late winter early spring, but if the road is open it could be a superb scenic drive with loads of snow on the mountains. It's a highlight of any trip to western Canada. But as Mariah says check the Fodor site.