Since the problems a occur in a number of appliances we can safely say your problem is low gas supply pressure, rather than blocked injectors etc. This can be caused by a number of things. Firstly, the gas bottle getting low, sounds obvious but as we know its not that easy to tell. Pick the bottle up and feel the weight, or swop to a spare. Second, could be the cold affecting the pressure in the bottle. At lower tmperatures gas contracts and the internal pressure reduces, and so the bottle behaves as if its empty. At zero degree centigrade the pressure of commercial propane is 4.5bar,and butane is only 0.9 bar so propane would be much better, I would suspect the use of butane is your problem given the weather. Shaking the bottle will agitate the LPG and therefore temperarily increase the internal pressure (like shaking a can of coke!)
Other things to consider could be a blocked or faulty regulator, just try it in better eather to diagnose this,and maybe small gas leaks from split flexible hoses or loose connections. corgi recommens replaceing flxible supply hoss every coupleof years or so.