No, running too rich would be black smoke, and burning too much oil would be blue.
Is it actually smoke, or does it dissipate after a few seconds? If smoke, that's probably coolant, and it indicated a bad head gasket which may be allowing some coolant into the combustion chamber. You would also tend to notice this because you would have to add coolant from time to time. If it's just condensation, which is a very normal byproduct from the exhaust, you don't have a problem.