Gelding later in life, like at age 12, can be an attitude change for some. Others will still act "proud"... Hence the term "proud-cut."
It would be smart on your part because you'll be able to do more with him, but he may still try to get through the fence to the mare. Remember too, it can take sometimes up to a year or more for a gelding to be completely sterile after neutering. If you're not particularly interested in breeding him, there's no harm in gelding. And I have never seen a mini with a bad mane and tail!!
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