Yes, and many Minnesota dogs have been injured or killed by lethal traps and snares. For example Scott Slocum's dog, Phillip, killed by a body-gripping trap on the frozen marsh behind their home in White Bear Lake, MN in 2012. You can read more about it in the CBS News article at http://minnesota.cbslocal.com/2012/01/28/dog-owners-speak-out-against-killer-trapping-method/
From 2012 until about 2021, the organization Dog Lovers 4 Safe Trapping MN advocated for improvements to the Minnesota State trapping regulations. The 2015 campaign was the most successful; although that year's bill wasn't heard by the MN House, it was approved by all of the required MN Senate committees. Unfortunately, it didn't advance to a Senate floor vote.
Lethal traps can be set relatively safely above the reach of dogs, or underwater where dogs don't swim, or in enclosures that prevent dogs from reaching the traps. Snares can be set relatively safely when their springs are removed, their non-relaxing locks are replaced by relaxing locks, and they're set to prevent tangling, hanging, or other complications.
Of course, in some cases, lethal traps and snares are necessary for nuisance-animal control. In these cases, professional judgement is required, to avoid sets in locations where dogs or other non-target animals might be injured or killed.
An answer to that question.
An answer to that question.