Only if it gets drunk, and it's not going to get drunk on a beer or two. Apparently even vets say it's not terrible for horses to drink alcohol since their gut has a weird process that we humans don't have. They can't get drunk unless you make them drink gallons and gallons of beer at once.
In one of his novels, Theodor Fontane describes a Prussian gentleman giving beer as a treat to his exhausted horse. As Fontane generally wrote about things he knew from personal experience, one may assume that this was common practice in 19th century Berlin!
Din/Dit/Dine is when you're speaking to one person, jeres is when you're speaking to more than one, or about something that a group owns if you're speaking to a person from that group. For example: Jeg elsker din hund = I love your dog (either it's only this person's dog or you don't know someone else also owns them)
Jeg elsker jeres hund = I love your dog (You might be speaking to the multiple people who own the dog or speaking someone from the family and know they are part of the family/it's come up in conversation.
Think of the difference like the difference between "your" and "y'all's" in colloquial southern US English