Hug Horny

Really wanting physical contact with someone that you highly value something as simple as a hug.

"Dude, is Chelsie alright?"
"I don't think she's gotten much attention from her boyfriend lately, at this point she's probably hug horny."

Horny hug

A horny hug is when you hug someone while horny and you both want sex

Person 1: Last night I gave Jane a horny hug.
Person 2: Well did you have sex?
Person 1: Yeah it was awesome!