Running wider tires in the front
This is not a problem at all. 

What you see quite often is that riders use tires with a lighter tread and harder rubber compound on the rear of the bike to get the benefits of good grip on the front and less rolling resistance on the back. A common example combination would be to use the grippy Schwalbe Magic Mary on the front and the faster-rolling Hans Dampf on the back wheel. 
(I am not affiliated with Schwalbe, I just don't know the names of similar combinations of other manufacturers.)

Sometimes, this also includes using a slightly thinner tire on the back wheel. A small difference is fine, though I probably wouldn't go as far as using a heavy downhill tire on the front and a skinny gravel tire on the back ;-)