Cold frame inside a cold greenhouse

Hope this is in the correct place. I am relatively new to gardening and last year I bought myself a strong wooden three tier cold frame and a five shelve plastic grown house. Unfortunately, even though the plastic grow house was tied down and had slabs on the bottom the thing fell over in strong winds and buckled which wasn't of any use thereafter. So, this year I've bought myself a 4x4 aluminium greenhouse, polycarbonate. Yes I know it's small, but I'm only intending to grow summer bedding plants and protect my tender fuchsias, I can always upgrade if needed right? (I can almost hear your screams "should have bought bigger"). Anyway, my question is .... If I put the cold frame containing my fuchsias inside my unheated greenhouse would this be suffient protection for them? I live in Dorset, and although we usually have it milder than the rest of the UK it was a very bad snowy winter here last year - the greenhouse faces SW.
Apologies if I've posted this incorrectly. Thank you.

 

Yes they will be fine down to -5, according to Monty Don. It`s the wind that does a vast amount of damage, so they will winter in your greenhouse very well.

 

Thank you Pam. In that case I can leave the cold frame out of my mini greenhouse as I'm sure I'll need the space eventually for something else.

 

"you should have bought bigger" I scream ...

Biggest problem with small greenhouses is the heat gain - when the sun comes out the temperature will sore - and if its on a day when you are not around the plants will suffer.

Small enclosures will provide no temperature gain over outside temperatures - i.e. the temperature inside will fall with only a small lag behind the external temperature - but that's true of large greenhouses too - if we get persistent cold of -10C over several days then the inside of my greenhouse will be pretty much down to -10C too. What does tend to happen is that the lag is greater [in a larger greenhouse] - so if the temperature falls to -10C at night, but during the day climbs to closer to 0C, then my greenhouse may only get down to -5C in the night before it starts climbing again during the day. As Pamsdish said the greenhouse will keep the chill / drying wind off them, and excess rain, but personally I would bring them in if the weather turns really cold. Snow is less of a worry than clear cold frosty nights - if the greenhouse is covered with snow it will insulate the plants inside better than a cold night with no snow covering.

The Fuchsias may be better off in a frost-free garage ... mine seem to survive OK with significant neglect over winter, but I do keep them frost-free.

Plan B would be to take some cuttings in the Autumn. They will be small enough, over winter, to remain crammed in with half a dozen in a 4" pot and then potted on as the temperatures rise in early Spring.