You could just keep your vodka/gin in the freezer, and mix it with vermouth. Why do people bother with the ice when making a martini? Ice just waters it down -- and if you do wish to dilute your drink, you can just add water to it.
The water, that is melted while stirring, is quite an important part of making a good Dry Martini. It helps smoothen the alcohol and changes the texture of the cocktail (alcohol, water and the mixture of both has a different viscosity)