Citation V pilot reported temporary loss of aircraft control while inadvertently flying into convective weather.

Narrative

I was seated on the R seat of a Citation 5 jet. Next to me on the L seat was the PIC manipulating the flight controls. He was navigating through an area of convective activity and later on to what it was referred to as part of hurricane Debby. ATC had given us clearance to deviate for convective activity to the L or R of course and so we did. Our ADS-B weather in the cockpit was not indicating any big cells ahead of us but there was a small area that appeared in our radar at our 12 o'clock without much notice; which seemed to be below our flight path.As we flew through the general area; our autopilot became disconnected and we encounter mod/severe turbulence with what appeared to be hail. The aircraft loss a total of about 1300 feet in altitude but was able to recover altitude after 20-30 seconds later. Similar weather was noticed in our return flight from ZZZ on Day 0 without having the autopilot get disconnected again. The aircraft did not suffer any apparent damage and they were no injuries to any of the crew or passengers.Later on; the mechanics reported that damage was found on the cone of the nose and both wings de-icing equipment.