It's intersting topic. Currently in Poland it's in the somewhat gray zone - you can lose licence and get heavy punishments for driving a vehicle when drunk, but horse isn't a vehicle according to the law definition (some paragraphs even specify "mechanical vehicle"). But in the road codex there are some exclusions where you can ride a horse or horse wagon, so you would need to pay attention to those. Also riding horse when drunk on the road would met the definition of "causing a danger in road traffic" and this is punishable too, though lighter than drunk drive.
Finally there is interesting loophole (afaik not checked yet) where a horse would go on autohorsepilot while the human would be lying drunk to total unconciousness on its back or in the wagon, so it would be unclear if he could be even counted as rider/driver.

Of course all this was nonsense in the relevant 70's/80's back then it was afaik legal and even if not, nobody i knew ever got into trouble for this. We also had maybe 1% of current cars so understandably the regulations were more relaxed and on such villages horse wagons and tractors were equally common sight as cars on the roads.