I'm sorry, but I wouldn't be looking to buy plug plants until late March. The weather is far too cold for an unheated green house and by buying later the plants grow on without a check. I would also try to keep them barely moist as the root system cannot cope with too much water. I would say that you need to carry on with growing them indoors, pot them on if they start to grow bigger. Keep them near the window light by day and move them away at night when the temperature drops. You could also place some aluminium foil the at the back of the plants to maximize the light.

I presume they are the bedding Begonias,and not the Tuberous ones,Bluewillow? Maybe they are damping off,if you have overwatered them..They will probably have been grown in a warm environment at the Garden centre,and too cold to put them in an unheated greenhouse yet,I think..

We crossed there,Jimmy the one..but basically the same reply..

Agree with J . The temp drop at the windowsill at night this time of year can be so fast and steep that it can shock the plugs. Place a thermometer at the sill to see this.

Agree with all. I do buy plugs early ( our garden centre sells them from late Jan), but I keep them in an insulated greenhouse, on a warming mat, covered, and in propergators all on capillary matting. I certainly wouldn't entertain them this early, if you don't have the facilities.
Also for begonia plugs, B.W., I never water from the top as this causes the plugs to rot.

Also I've found that they grow very slowly until they get going. When you say not doing so good, what do you mean exactly?

Thank you everyone for you replys,i think I might have over watered them a bit, as one seems to have collapsed and died, should I put them in a heated propagator? and stop the watering for a while? how much do I need to water them as they being so small?,thank you again.

No rules. You water them when the compost begins to look dry. It is easier to rescue plants wilting through under watering than over watering. If you put them in a heated propagator they probably won't need watering very often. Just make sure the mat underneath is kept damp. Andmake sure you leave a ventilator open at least during hte day.

An afterthought - if more begin collapsing near the first one you have a damping off problem and you need to treat with a copper based fungicide.