depends which plants they are. If they were the sort of plants that are put in winter tubs then they will be pretty much ok.

Can you give some more info please.

Yes you should be ok, I have many varied shrubs in pots and tubs etc, inc many of the Bamboos, over the years when we have had heavy snowfall I gently knock of the snow,I do this so that the weight does not snap any of the stems and if it freezes after snowfall then this can be more of a problem to the evergreen plants, depending on the type of plants you give them some protection, note if we get a prolonged cold snap with sub zero temps then I would protect certain plants eg Hebe,s can suffer in harsh conditions.

Snow is an excellent winter mulch for many plants.

a bit of snow on plants in pots is not an issue, provided you don't allow a deep build up on bushy evergreens, when they might break under the weight. The issue with plants in pots is if the temperatures fall below zero degrees day and night for longer than a week, when the pots may freeze and the roots will be destroyed. Although we've had some snow, the temperatures certainly have not been low enough for any length of time for that to happen.