If your course gets boggy then hedgehog type wheels are the spawn of the devil. They will sink in and gather huge amounts of mud, which will then cause loads of spinning of the wheels and more damage to the grass. At the end of the round there'll be a one inch "tyre" of mud around the wheel.
On the other hand if the course stays firm, hedgehogs are great. They minimise contact with the grass and will reduce spinning and tearing.
Unfortunately I play at a boggy course, and we have frequent trolley bans in winter :-(
The course drains extremely well and is limestone based. There has been possibly too many visitors to the detriment of members. I am talking of hedgehog wheels but we have only been advised today and I think it has a bit to run. There is the option to carry or use a trolley with a medical certificate. They do not want to bring in fairway mats nor play the ball from the semi rough.
The idea is to protect the course during the wetter winter months from December to March.