Not too bad, I guess. People do this all the time in the hobby/maker world. The thing is you need to have the materials and know-how to do it. Are you asking is it possible, or are you knowledgeable enough about how it could be done but are asking if it's practical/easy enough?
Search around makezine.com for projects with Arduinos and wifi cards. The most/only one used is the Xbee wireless card, often with the helpful adapter to facilitate communication. You could also use an ethernet shield/addon, but that would make it wired. Unless you used the FRC robot radio...
http://www.ladyada.net/make/xbee/
(the ladyada site is extremely good, look at their tutorials and shop, too)