A pump is likely to be part of your regular reinforcements, but when was it last serviced? Disassembling your pump and checking its innards are free from moisture and debris is time well spent and should be included among more obvious preparations for winter riding. The last occasion on which you’ll want to discover that the seals have perished when stood at the roadside 60 miles from home.
Avoid the temptation to wash the bike with the pump in situ. There is perhaps no easier way of degrading its constituent parts. When you’ve cleaned the pump’s internals, add a small dab of silicone grease to the rubber o-ring to protect it from moisture. If the seal has perished, service kits are available from manufacturers for little money. While on the topic, it’s also worth checking the condition of the spare inner tube in your seat pack. Confined in a tight space, frequently shared with sharp-edged metal objects like a multi-tool, a tube can easily become damaged.