Hi Qantas_A380,
I think what happens is this: The ice buildup rates temporarily exceed the capability of the anti-icing pitot heater. The entrance to the pitot tube is blocked, but the pitot probe drain hole remains open. The sensed Pt drops quickly towards static pressure (Ps). The IAS drops quickly towards stall speed (or stick shaker if one is present), hence the stall warning. The IAS remains affected, usually for a short period, until the heater catches up once again and the blockage is cleared.
I don't know exactly why nose up occurs in some situations, each one may be different depending on what the crew observes and decides to do. For instance, if the crew decides they need more power to overcome a perceived stall, they may apply TOGA thrust which will cause a pitch-up in aircraft where the engines are mounted under the wings. Anyhow, I hope this explanation helps…