If you could get past the locked gate where the road from the campground ends and the road to the lake begins.....maybe if you had 44's with lockers, chains and a winchIs it not accessible in the Winter with an SUV?
Seriously, they lock the gate to autos (or did the last I knew of), you can run a snowmachine up there, but the road drifts in some places and is bare pavement in others so it's hard on things with tracks designed for snow.
If you want lakers thru the ice I'd look at Green Mountain, Granby or a couple other spots you can get to more easily.
Jefferson is a beautiful place though and I enjoy going there too.
***On a side note a long time ago before they closed stuff down I made a run up there in late December in a 1970 Bronco, heavily modified along with some folks with a full size p/u with 38's, it was a real butt puckering experience and I vowed to never try that again.