You cannot always take transcriptions for granted, that they are correct, you should always check the original entries. Mistakes can occur in those as well, many census, particularly the earlier ones, relied on what the enumerator was told & what he thought he heard, then mistakes took place when they were copied from his entry books to the records. We have to take a broad view of what we see in transcriptions & work out what best fits what we are looking for.
I cannot tell you just from looking at the 1901 census whether the entry for Arthur Sidney Winter is the son of William & Martha. To find out whether he is or not you would have to find & buy the marriage cert, this will tell you his father's name.
This should help
Marriage
William Sidney Winter = Bertha Marsh
Dec ¼ 1892 Lambeth 1d 692
1901 census info
On the same page & living in the same street as Arthur Sidney Winter is a James G Winter born 1858 Westminster
RG13/427 folio 161 page 17
12, Vicary St. Lambeth, Brixton
James G. Winter head age 43 Housedecorator b Westminster
Hannah wife age39 b Marylebone
Richard J. son age 15 Printer's Labourer b ditto
Ethel M. dau age 12 b St Pancras
James G. son age 5 b Grays, Essex
Laura dau age3 b Hammersmith London
William E son age b dittp
16, Vicary St, Lambeth , Brixton
Arthur Sidney Winter head age 39 ironmonger b London
Bertha wife age 29 b Whitstable
Eric M. son age 7 b London
Reginald son age 5 b ditto
Kate Marsh, sister in law age 14 b London
In your request posts, if you have found anything in any of the census, please post the Distict, Piece no, folio & page no, this eliminates anyone wishing to help having to spend time searching for it.
Meliora