I am using ASP.NET. I either add or set a cookie (depending on whether the HttpRequest
contains a cookie with specified key), and immediately afterward call
After googling a bit it seems that yes, there can be problems with setting the cookie in the redirect response as it may be ignored by a few browsers. (It may make some sense, as the response is really telling the client to ignore the resource and get some other resource instead).
This has been discussed here already: Sending browser cookies during a 302 redirect
So I would change the architecture in a way that allows the page being redirected to to set the cookie.