The thing I have to ask about this is: What problem does it solve?
It's pretty clear that there would be quite significant disruption and expense involved in converting from one type of 3rd rail to another. I'd guess there would be years where not all units could run on all lines (ignoring the current AC vs DC situation, as this would not change that), individual lines taken out of service for extended periods, inevitable teething troubles after each conversion giving intermittent issues for months, etc.
So, what is the perceived benefit gained from going through all that disruption? Safety? Bottom contact 3rd rail is still quite dangerous, needing to be treated with much the same care, and the rails would likely be much higher and therefore a bigger trip hazard. Just how many serious incidents would it prevent? I'm guessing that the number of incidents caused by the current 3rd rail setup is so small that it's really not worth the disruption.
I can see reasonable justification for wanting to convert some lines to OHLE in the medium to long term, but I just can't honestly see any justification for changing the style of 3rd rail.
As far as snow and ice goes, there are solutions to deal with that on the current infrastructure, we just need to make sure that they are available and used.