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Hi. My name is***** thank you for your question. This cream shouldn't be that critical for him to have had some possibly transfer onto his fur. There are a lot more serious potential situations with other specific medicated creams. As far as for him, you could take a warm, damp wash rag and just wipe this over his fur. This can help to get some (if any transferred) of it off him. You could then brush him really well to help get any lose fur off that may hold any more. More than likely this isn't again going to be an issue. If you want to let him have good access to water as this may help to wash any out of the oral cavity if he groomed himself and has some in his mouth. If he starts to vomit or not eat in 24 hours, then he should be checked over. The stomatitis he has most likely won't be aggravated by this. It may be the stomatitis itself just getting more progressed and needing to be addressed.
Cold weather itself shouldn't have an effect on a stomatitis situation. Stress though could cause it to not do as well. If he's staying with you in a new environment, the stress of that can sometimes allow these situations to get more pronounced.