It is possible to start some early sowings in January. Tempting though this is you there can be problems. Early in the year the young plants cannot go outside, potentially for several months which means space is needed to grow the seedlings under glass to protect them. Everything which you sow now/or buy from the garden centre as a plug plant, will have to be grown under glass until frost is over. If space is short it's best to wait until later in the year.
It is also still cold and to germinate seeds need warmth, such as a heated propagator and then transfer under glass. Once established the seedlings should be OK in the greenhouse, unless it is very cold, when cover with a fleece.
A heated propagator mat is good if you want to get seedlings going early. The average conservatory/greenhouse is too cold to germinate seeds, and this heated aluminium mat (illustrated left the propagator trays stand on it,) is ideal to start germination. More Advice on how to germinate from seed and a short video looking at growing veg from seed.
One of the main problems growing seedlings at this time of year is not just the cold, but also low light levels. This can cause seedlings to be spindly and leggy. Often light is from one side only, and the seedlings become leggy growing towards the single source of light.