After your first few hours of upper air work a lot of time will be spent in the "circuit." With a suitably qualified instructor this would require a cloud base of just over 1000 feet and reasonable visibility. Light rain is not a problem. That description translates into pretty poor weather.
Fog, gales, heavy rain and cloud down to the hilltops will stop you flying
Navigation training requires better weather than that, however the lesson can often be modified to suit the weather on the day. This may depend on the experience, qualifications and determination of your instructor.
Wind is the other major weather factor. Light aircraft can fly in fairly strong wind (if your stomach can) but if the wind is strong, and across the runway the lesson may be cancelled. Now you are thinking "where can I learn that has a choice of runways?"
Back to the subject of cancellations. This can be caused by mechanical issues. Is there maintenence on the airfield? Are spare aircraft available?
D.O.