As others have pointed out, the road bike position isn't the same as MTBs. The wrong position will hurt a lot more, too, because you're generally on the bike for longer and don't stand up or move about as much as off-road.
As to specific exercises, here's one from my physio which cured my sore forearms a couple of years ago. Sit in a chair with an arm rest and position your arm so that the wrist bones are just beyond the end of it. Hold a 16oz tin of beans/whatever lengthways between your thumb and little finger. Keeping your arm flat, steadily lift and lower the hand to full extension and keep repeating it until you get bored with what's on the telly.
After three weeks of building up to 50 reps on each wrist before it hurt, my sore forearms were back to normal and I've never had the problem since.