this could be any number of things, start with the cheapest ones to do, and go from there, a mistake many people make is to put oversize rims and tires on a vehicle, this can bite you in the butt later when it starts wearing out the bushings in the front end, and all the tie rod ends and ball joints as an example. The first thing I would do is go down to a tire store and have my front tires only rebalanced, and have them check to make sure the rims are not bent and wobbly on the machine as they balance the tire. Also , ask them for a free front end inspection, and make a written estimate of any problems. If the front end is tight and the rims and tires are balanced, and there is still a wobble, next, make sure there is no play in the steering box,some of these can be adjusted. If all else fails, you may have to spend a couple hundred bucks on a steering damper. We used these in the past to take vibration out of big oversize tires.
Sometimes, a rim and tire just dont balance right for what ever reason, some tire guy can bust a tire loose and spin the tire 180 degree on the rim and air it back up, or balance the back two tires and rotate them to the front. If its pretty much one speed all the time, like everytime at 62 mph, that is most likely a tire balance issue, some guys, and some machines are bretter than others too. good luck.