Okay, so in Frosty The Snowman (1969) the answer is inconclusive – the hat is either always on his head or out of his possession entirely.
But in Frosty’s Winter Wonderland (1976), the kids make him a snow-wife and she comes alive through ‘the power of love’ when he hands her a bouquet of flowers he made out of snow. A short while later, he gets attacked and his hat gets blown off, but instead of getting the hat back his snow-wife makes a flower for him, sticks it in his buttonhole, and brings him back to life with ‘the power of love’ too. So, yeah: two sentient snowpeople, both hatless.
spoiler
(At least briefly: he almost immediately gets the hat back anyway.)
Also: they ask the parson to officiate their wedding. He’s too racist against snow-people to be willing to do it himself, but, inexplicably, he’s happy to help make a snow-parson to officiate instead. They bring that one to life by giving him a Bible. So at that point the whole thing’s off the rails and who knows what the Hell the rules are. Frankly, I’m not sure that sequel should count.
Okay, so in Frosty The Snowman (1969) the answer is inconclusive – the hat is either always on his head or out of his possession entirely.
But in Frosty’s Winter Wonderland (1976), the kids make him a snow-wife and she comes alive through ‘the power of love’ when he hands her a bouquet of flowers he made out of snow. A short while later, he gets attacked and his hat gets blown off, but instead of getting the hat back his snow-wife makes a flower for him, sticks it in his buttonhole, and brings him back to life with ‘the power of love’ too. So, yeah: two sentient snowpeople, both hatless.
spoiler
(At least briefly: he almost immediately gets the hat back anyway.)
Also: they ask the parson to officiate their wedding. He’s too racist against snow-people to be willing to do it himself, but, inexplicably, he’s happy to help make a snow-parson to officiate instead. They bring that one to life by giving him a Bible. So at that point the whole thing’s off the rails and who knows what the Hell the rules are. Frankly, I’m not sure that sequel should count.