Visit to Madinah for Ziyarat

yes you can visit medina for ziyarah and can do umrah too. hurry up and perform your umrah as hajj pilgrims started arriving mecca and medina and it will get more difficult to perform umrah near hajj days.

I am heading madinah soon - you wanna join?
Shaheer

If you are on visit considering Hajj season the police at check point (just incase they check - theyget more vigilent in Hajj season) might refuse as you're on visit visa. often visit visas issues during this season says not valid for Hajj/Umrah. Does your visa say so?

Well I think going for Umra now won't be recommended due to checking and no accommodation (all hotels reserved for Hajj pilgrims)
However you can plan for Madina, 1 day visit will be feasible in these days as it's very likely that you won't find any accommodation till Hajj concludes.