I don't really think the question is ambiguous. The most likely real-world context is that the questioner assumes it's going to be cold tomorrow, and that there will be precipitation. He's just asking if that precipitation will be rain or snow.
If we're to admit of any other interpretations (i.e. - it's ambiguous), we must accept that there are several questions being asked at once...
1) Will it be cold?
2) Will there be precipitation?
3) If it's cold and there is preciptation, will it fall as rain or snow?
Note that in my straightforward interpretation, it's always possible to disagree with either of the assumptions, by answering negatively to either of the questions (1) or (2) above, even though they've not been explicitly asked.