I see where you are coming from with wanting to get your boy exercise...it is really important. Hopefully your rain will pass, and he will get out to play more. I think if you at least keep him engaged mentally, and practice your in hand work, it will keep him occupied through the rain.
Yeah, if you could get him out ponying on the trail, or even ground driving on trail, I am sure he would LOVE it - and what great prep for when he gets ridden later!
I remember talking to someone this summer about the Deb Bennet books on horse structure and conformation, and discussing how new research is showing that the backbone on a horse is one of the last things to develop, and is not fully developed until around age 6! To think, we are sitting on and being supported by an undeveloped part of the horse for years, even those of us who start later.
When to start horses on different things in their training has and is quite a controversial topic...I would personally err on the side of waiting longer to do things rather than risking the long term health of my horse (and as I learn more, this belief develops - I rode my six year old a bit more as a two year old than I think I will do with my horses in the future - to no ill effect that I can see now, but why risk these things).
Sorry for the tangent...