If you've got a blog or a CMS, consider adding a message to your website that tells your customers when you're open this Christmas, or about any changes to your normal operating times / services due to the snow.
If you don't have a way of updating your site yourself, then drop us an email and we'll help you out.
If you run an online shop and the phone is going crazy with people ringing asking whether they can expect their order before Christmas, maybe send out an email to your customer mailing list explaining the situation. If your online shop includes user accounts that shows an order's status (pending, dispatched etc.) include that information in your email so people can check their account to see if their order is on it's way.