This works:
all.vars(formula(Model)[-2])
## [1] "var1" "var2" "var3"
The [-2]
indexing removes the response variable from the formula. However, you may be disappointed that the internally stored model frame does not have the original variables, but the transformed variables ...
names(model.frame(Model))
## [1] "Class" "addNA(var1)" "var2" "log(var3)"
If you want the raw names, then all.vars(getCall(Model)$formula)
should work.