Can a Ohio eviction proceed during winter or holidays?

Generally yes, but with practical limitations. Ohio does not have a statutory winter eviction ban (unlike some European jurisdictions). The notice period (3 days for pay-or-quit under ORC 1923.04, with mandatory verbatim 'you are being asked to leave' language) and court calendar continue regardless of season. However, in practice: courts close on federal and state holidays, sheriff's offices reduce service hours during the last two weeks of December, and some Ohio judges exercise discretion to delay sheriff lockouts in extreme weather. A landlord should NOT count on holiday delays preventing eviction; serve the notice on the same timeline as any other month. If the tenant has a habitability counter-claim involving heat, holiday-season cases get more sympathetic treatment from juries and judges. Plan filings to avoid the December 20 to January 5 window if discretion is anticipated.

Source: Ohio unlawful detainer procedure