A321 First Officer reported autopilot failure on climb; with the aircraft reporting a Flight Control Alternate Law ECAM Caution Message. The flight crew communicated with Dispatch and Maintenance Control and elected to divert.

Narrative

We planned to launch from ZZZ to ZZZ1. The weather was low IFR due to a snowstorm that spanned most of the mountain region. There was significant ice on the airplane as it had sat for the previous 12+ hours in this snowstorm. During walk around; there was a truck at the gate to de-ice the airplane's windshields and engine inlets. I was told we would receive the remainder of de-icing completed at the pad. We arrived at the de-ice pad and it took more than an hour for de-icing to be completed. After takeoff from XXL; we entered the clouds fairly quickly and attempted to engage the Autopilot - it did not work. We then attempted it again; and shortly thereafter received the Flight Control Alternate Law Message Caution on the ECAM display. We executed the standard ECAM procedures and noted no follow up actions for this ECAM. No others information was available to troubleshoot the procedure and no background information indicated why the aircraft had reverted to Alternate Law. As we continued our climb; the Captain transferred controls to me while he began coordinating with Dispatch and Maintenance to further determine what was wrong with the aircraft and to develop a game plan. We leveled off at FL230 to initially remain in clear air and avoid climbing into RVSM since we did not have a functioning Autopilot. Due to snowstorms throughout the plains region; the Captain coordinated with Dispatch for a suitable divert and briefed the Flight Attendants on our situation. We chose ZZZ2 for our divert as it was the closest field with suitable facilities that was not under winter IFR conditions. In-flight; we discussed; ad nauseam; the procedures for landing in Alternate Law; including considerations for reversion to Direct Law once the landing gear was lowered. Enroute; we [requested priority handling] and coordinated with applicable ATC agencies. After setting up the aircraft for our divert; the Captain assumed flying duties once again; and we eventually landed in ZZZ2 without incident. Upon landing; we received additional ECAM messages for CAPT AOA Probe and FO AOA Probe. These messages were never displayed in-flight. At several stages of the flight; the emergent situation was worsened as the Captain and I were still familiarizing ourselves with several procedural changes that were recently implemented outside of training cycles. In most cases we've found these changes to be minor; however the added stress of dealing with a flight control malfunction while digesting new call outs and altered habit patterns was non-ideal.Failure seems to be related to a mechanical failure of both AOA probes. I assume the likelihood of this occurring is low; and therefore this could potentially related to ice accumulation on the aircraft prior to departure.