The only negative that I can think of is an increased likelihood of stepping into a trap if trapping is legal in the area. While it is easy to find incidents of pets getting caught in a trap, there are reports of people getting caught in hunting traps too. Trapping is a charged topic, and there are even sites against trapping which purport to have lists of incidents. It seems like children are particularly vulnerable.
None of those incidents that I linked are strictly related to walking game trails, but traps are often placed in areas frequently traveled by the targeted animals so game trails logically are potential trapping locations. When I'm walking around I typically don't worry about traps, but it is something to be aware of, especially if you are with young children or pets. Then again I have never frequented areas where trapping was common. If you do live in an area that has trapping be vigilant, and if you see one trap assume others are around.
Overall I wouldn't consider this a deterrent unless the area was a known trapping area, and I had a curious dog with me. If both those conditions were true I'd probably stick to established trails. Otherwise, I say go for it!