Can a Texas eviction proceed during winter or holidays?

Generally yes, but with practical limitations. Texas does not have a statutory winter eviction ban (unlike some European jurisdictions). The notice period (3 days under Tex. Prop. Code 24.005, unless the lease specifies longer) 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 Texas 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: Texas unlawful detainer procedure