I've been diagnosed with Raynaud's and get cold feet/legs, cold hands, and cold nose. Even my ears get bright red at times, but not sure if that is from Raynauds. I have a very lacy looking patter in my legs and doc says that is classic Raynauds. I never really noticed color changes so much, but mine is wide spread so it's not as easy to tell. I've also noticed that the cramps I get in my feet and calfs are worse when my legs/feet are cold. If I take nifedipine, the cramps go away as well as getting warmth back in them. I've seen pictures where 1/2 your finger can be white, then the other half blue...I'm not like but more like patches of discoloration..I still think it can vary, but that's just my opinion. I haven't had much with pins and needles, but I get stiff and achy when Raynaud's flares up.
If your feet are cold after sitting, it could be a circulation problem. I have BP that is too low and blood that pools, so if I sit too long, my feet get cold. I also have Raynauds, and that's totally different. When I'm out in cold air, my hands go completely white, then as they warm back up, they hurt and burn like nobody's business. Pins and needles doesn't even begin to describe the pain. They also get red as they warm up.
Your thyroid can also cause similiar issues. You might want to get that tested.
As I understand it, to be Raynauds there has to be color change. I have Raynauds in my hands, with color change. I also get cold feet with no color change most likely due to poor circulation.