I have owned a 2013 Raptor for 3 weeks now.
Short Answer:
Heavy snow and ice: Raptor don't care. It does whatever it wants.
Snow and ice covered road: Raptor don't care. It does whatever it wants.
Long Answer:
First, the Raptor has the ability to lock the rear differential. This will provide maximum traction in those difficult spots. Depending on your Off Road setting, it will disengage at certain speeds.
The Raptor AdvanceTrac has three settings: Normal, Sport and Off. This will impact the traction control and yaw in the truck. If set to Off it will revert to Sport over 35 mph unless the Off Road setting is On.
Lastly, the Raptor has an Off Road setting. It is either "on" or "off". The Off Road setting and AdvanceTrac combined will drive the Raptors traction control and yaw.
I'm impressed with the AdvanceTrac. It was extremely difficult to break the truck loose on snow covered roads....even when I tried. I had a 2006 F150 before this. It did great in the snow but the Raptor has been even better.
You can definitely use your 4 Wheel Hi on snow, slush and ice covered roads. That what it's for!!
I can't speak to towing. Sorry