I've got a vintage 1965 Beetle (1600cc engine refurbished).
Its winter now - and I'm finding that the Beetle has no power when I shift to 2nd gear - even after a few minutes after turn key.
Is it a common problem? How can I fix it.
I dreamed of putting a hair dryer inside the Beetle bay - and flicking it on to warm up the engine.
pre heat tube on mainfold may be blocked
After the car has warmed up, spit on your finger and put it on the preheat tube, the preheat tube should sizzle your spit. what sort of carb setup are you running?
Touch the underside of the centre of the manifold and once warmed up you shouldn't be able to comfortably touch it for more than a sec or 2. Touching the heat riser right up by the manifolds centre works for the spit test but even half way up thermal transfer could have warmed the tube enough even if it's blocked.
Or some people dont have heat riser tubes at all 
I used to run a Holley bug spay on a Beetle years ago, it would turn into a block of ice this time of year, I greatly improved it by sticking an ice cream container on top of the air cleaner so that it would only suck air from the crankcase and not fresh air and a further improvement was fitting the stock air cleaner heater tube and fitting into the ice cream container
I remember even on a water heated manifold of an 80's hot hatch i fitted a 32/38 DGAV too that due to the K&N filter it would freeze up in the
dead of winter after 10 mins on the motorway 
lol the perks of carbs ey
I used to own a dead stock 2.6 Sigma wagon in the 80s, one night near Oberon the carby froze, I just took cold air snorkel off and it was OK, lucky I knew the symptoms from my Bug spray experience
On a VW at work, I said to the restoration manager "Has anyone checked the pre-heat tube for blockage?" He asked me to check, and I found the entire straight section was blocked. I used a pneumatic hammer to 'rattle' the whole tube section and after a while the coke all shattered and came out. I could get a rubber hose of similar size to the internal diameter of the pre heat tube to go through the whole pre heat tube, so I surmise that it was pretty well cleaned out.