Do reindeer have (a) sex?

I had no idea but apparently every year at holiday time the innernetz buzz with debate about whether Santa's reindeer were male or female. I thought it was clear it was a unisex team but experts present solid arguments for all-female, all-castrated males or all-bull teams, though they maintain the bulls would be too exhausted for sleigh-pulling due to rutting season. I'm imagining reindeer bulls sitting around watching bowl games and saying 'Beer me!.'