Unfortunately you cannot create new commands by adding a snippet, as you have found. The refactoring snippets are there to help you control the refactoring commands, but extra work has to go on in the background to enable the reactoring to work.
Here you either need to swap between two different sets of code for the Encapsulate Field snippet, as you move between C++ and C++/CLI, or use a separate snippet for one of these two languages. Perhaps starting with:
void Set$AccessorName=$clipboard$$($dataType$ data) { $clipboard$ = data; }
$dataType$ Get$AccessorName=$clipboard$$() { return $clipboard$; }
something similar would help here. Here the thinking is that the member variable is in the clipboard, and you can then use this as the start point for the function names. You still need to enter the variable type, but you can use the clipboard history menu to help here, if you copy this before copying the variable name.
We are considering adding the ability for normal snippets to work out and insert the type of a variable, but I don't currently have an estimate for when this might be done:
case=5472