In addition to tours and attractions not being open, most RV parks and government campgrounds aren't open either. Overnight temperatures may be below the freezing, enough to freeze water in the RV. Snowfall is a possibility in April too, so be prepared to wait out a storm.
I drove from Anchorage to Whitehorse on March 28 this year, see those pictures
http://yukonsights.ca/20140328_Anch-Whrs.htmlIn 2013, we RVed to Liard Hotsprings at the end of March 2013 and drove the Alaska Highway to Whitehorse on March 31.
http://yukonsights.ca/20130331_Liard-Whitehorse.htmlAnd the first week of May 2013, an RV trip to Faro, Yukon
http://yukonsights.ca/20130503_Braeburn-Faro.htmlSome images of Yukon from mid-April 2013 here.
http://yukonsights.ca/20130414_SpringYukon.html