I've been planning on adding a mulch circle around my trees for a while now and have time to do it this weekend. I've been reading that you shouldn't butt the mulch directly against the tree, as the humidity can cause rot in the trunk. Looking at the trees however, I have several with roots that come back up out of the ground and are exposed. Does mulch present the same hazard to them? Should I avoid covering them?
If they are large, buttress roots, no you shouldn't cover them. If they're smaller roots, you can put a thin layer of mulch over the top, but not thicker than around 1 inch, 2 inches as an absolute maximum - but it is dependent on what type of roots are above soil level, so a photo or two might be useful. Further information on this subject here https://www.thespruce.com/will-soil-over-tree-roots-hurt-tree-2132816