Robin Milner, 49, of Sherburn in Elmet, was arrested near the Swan Hotel, Low Street, South Milford at about 20:00 BST on 30 July.
He told York Magistrates' Court he had "participated in a few beers" at a christening earlier in the day and had not realised he had drunk so many.
Milner was given a conditional discharge for six months and ordered to pay Â£105 in costs.
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Magistrates told him they appreciated his guilty plea and the fact he had co-operated with police when arrested.
Milner, who represented himself in court, said he believed he had about four pints.
His cart had scratched a man's car in the car park of the Swan Hotel and the two men were exchanging details when a police officer noticed the defendant appeared to be drunk.
A man has admitted being drunk in charge of a horse and cart.