Why a cover often makes things worse, not better
The instinct to tarp or cover outdoor furniture for winter comes from a reasonable place — it's protecting the furniture from weather. But a cover creates a dark, still, weatherproof void directly against or under the furniture, which is a close match for what a mouse looks for once temperatures drop and outdoor shelter options thin out. The cover keeps rain off, but it also keeps a mouse hidden from view and from predators while it works through cushion foam or fabric.
A Cooperative Extension response to homeowners asking almost exactly this question is direct on the point: 'leave the furniture uncovered as much as possible' (UMD Ask Extension). That's a counterintuitive answer, and it's worth taking seriously precisely because it runs against what furniture-care advice usually says — an extension horticulturist is optimizing for the pest risk here, not the furniture finish, and for winter storage the pest risk is the bigger problem.

