In AmE, writer and rider are generally not distinguished unless the dialect in question happens to exhibit Canadian raising. Note that despite the name, Canadian raising is not exclusively Canadian, and you can find speakers exhibiting it in the US as well. The difference isn't in the "w", though--it's in the first vowel. See the Wikipedia link for details.
In addition, there may be a small difference in the length of the first vowel in AmE. According to Peter Shor's comment, you can find this difference in most American dialects, but as I understand it there isn't generally a large enough difference to reliably distinguish the two.
In BrE, /t/ and /d/ sound different, so writer and rider sound different.