I am not a Husky guy, but Your question just as well relates to any other brand.
Other then increasing the gauge to .058" or .063" in order to increase/improve lubrication I don't see any problem running 3/8" on a 36" bar.
I think I read some run 3/8" LowProfile for milling, I might be wrong though.
I run 3/8" .058" on my 36" bar and my Dolmar PS-7900 is pulling it very well.
3/8" .058" is my chain preference for my everydays B&C setup, thus I opted to keep it simple when I purchased my 36" bar.
As mentioned, You may experience stronger chain stretch.
Other then that keeping 3/8" .050" shouldn't be an issue.
The above is just my humble opinion.