As @Erik notes, the answer to your question is vacuously "yes".
Digging a little deeper, we can break this into two questions:
Given the vast amount of weather data available (http://opendata.stackexchange.com/questions/10154/sources-of-weather-data/10155), is it possible to find correlations (either linear or non-linear) between known data such as latitude, longitude, elevation, time, previous weather (temperature, pressure, etc) and current weather? Of course, your interest is in correlating present conditions to future conditions, but, since we're looking at existing data, this is the same as correlation past conditions to present conditions.
If such correlations exist, can we use them to predict future weather?
The answer to the first question is definitely yes: there necessarily exists a mathematical function that will convert any finite amount of known data and past conditions to present conditions. However, this mathematical function may be extremely complicated and completely useless for future predictions.
The answer to the second question is "maybe". We can limit ourselves to "simple" correlations derived from a given set of data and then test our correlations against out of band data (ie, data not used to create the correlations), or, better still, to make and test actual predictions.
Since correlation doesn't imply causation and past performance doesn't imply future performance, there's no guarantee that this will work.
In some sense, the following questions ask essentially the same question:
and probably a few others.
I think this would make an interesting project, but I don't know to what extent anyone has pursued this. If anyone wants to pursue it more deeply, feel free to contact me directly (contact info in profile).