V1mcg is the minimum speed (on ground) at which the aircraft is controllable by aerodynamic means alone (no credit for nosewheel steering). As it relates to countering
asymmetric engine thrust, it is fundamentally a function of temperature and altitude - i.e. it is independent of
friction characteristics between tyre and runway.
On a contaminated runway, there are two forms of additional drag to consider:
displacement drag and impingement drag.
The former is about the additional drag caused by the force required to move the contaminant from the
path of motion. The latter is about the force on the airframe from airborne contaminant.
The deeper the contamination on the runway, the greater is the
physical resistance to lateral deviation (displacement drag) following engine failure and therefore a weight
"benefit" with increased contaminant depth.
I hope this has been of some help to you.
Cheers Mangatete.