Emoticons are not used in formal writing, so how they are punctuated is really just a matter of style choice. It depends on how you conceive of the function of emoticons.
We can think of emoticons as a parenthetical expressionparenthetical expression of emotion that helps the reader to understand the text (e.g., "(I feel sad.)"). In this sense, they are rather like stage directions in the script for a play.
Since emoticons are extraneous to the meaning of the sentence and can stand on their own, I would suggest only punctuating the sentence proper.
He probably caught his cold from the kids at school. :( I hope he feels better tomorrow.
This would be roughly the equivalent of
He probably caught his cold from the kids at school. (I feel sad.) I hope he feels better tomorrow.
If instead you feel that an emoticon instead represents terminal punctuation (e.g., a sad exclamation point), as some commenters have suggested, then you would leave off the period altogether since further punctuation is not necessary.
He probably caught his cold from the kids at school :( I hope he feels better tomorrow.
In any case, I think it would be improper to put a period after the emoticon.