Cheap wine is expensive on A/C, too!!!!!
1.5 liter jug of Carlos Rosini was $34 US!!!
Glasses of wine at bars were $4 US.
You should have no trouble with wine at customs.
The Belize Customs web site tells you that you can bring 1.5 liter of alcohol. HOWEVER it does not specific what kind. My husband's case of Bud was taken when we came in July. BUT they let us pick it up on our way home. It seems beer interfers with their commerce.
The wine that I brought was no problem. But they didn't at any other bags after the Bud.