The honest answer is it's a crapshoot. Snow is not uncommon on the North Rim in April. You should be prepared (and I MEAN prepared) or anything from ice to mud. There are times when the road is only passable before it melts for the day.
On the otherhand we've experience some of the most amazing, if still cool, weather in April.
If it falls apart, northen AZ has some real nice adventures around Sedona and the Bradshaw mountains around Prescott. Google Sedona off road trails, Back road to Crown King, Smiley Rock, Senator Highway, Bloody Basin.
Best answer I can give. Sorry.
Paved roads are just for getting you to the starting point!