James and the lad are walking across a green field and suddenly through deep snow.
It is not physically possible for weather to change that quickly in that space of time.
Often regarded as a goof, the scene where James and Wes walk through the green field and then the snow is not a mistake. The Yorkshire Dales can see all weathers in one day. Also due to the Dales geography, one valley can be deep in snow, the next nothing.
When James and the lady from the RSPCA go looking for the dog, James goes to a lady and knows that she's a relative of Wesley. He didn't meet her on the last visit, so he wouldn't know who she was on this visit.