Is it rude to ask the status of an application? I have applied for a PhD position in October 2015. I was not informed about the result since then.

Is it appropriate to send a mail to a member of the hiring committee (with whom I have contacted before applying) to ask about the process? Or should I wait for them to contact me?

The university is in Sweden and I have contacted with the member prior to the application since he is the head of the research group that I intend to work in.
I don't think it is inappropriate nor rude to send them an email. It's your right to be informed with your result as time is passing.