On the scale issue, the Wall is almost exactly 300 miles/100 leagues, so you can just use that as a scale bar. The continent as a whole is about 3,000 miles from the Wall to the south coast, with roughly 700 miles north of the Wall to the top of the maps in the books.

the time for traveling was too short considering the difference of climates between the regions
The books are very ambiguous on travelling times for this reason (it almost 3 years between the start of the first book and the end of the fifth book, which is rather more than I think most people realise). After - quite literally - years of studing this issue over on the Westeros forums, the consensus is that the travelling times/distances do work out as broadly correct.