There are several strategies and products to replace older windows without having to remove any trim, siding or drywall.
Several window manufacturers make complete double-hung replacement window units that come without exterior trim and that are engineered to fit INSIDE the jambs of an old double-hung window. They are custom built to fit exactly into the existing opening. The result is more energy efficient, more functional, and, usually, more attractive.
You pull out the old sashes and stops. You remove any springs, ropes and weights that operated the old sashes. You can fill the old weight pocket with insulation.
Then you insert the unit and secure it to the existing jambs. They generally have trim pieces that will cover the gap between the new unit and the trim.
Replacement Sash Kits
A variation on a complete window insert unit is a system that comes with two double-hung sashes and detached tracks. Like a complete insert, these fit INSIDE the jambs of an existing double-hung window.
Once the old window and stops are removed you fasten metal brackets evenly down the window frame and snap the vinyl jamb liners in place.
The new sashes will tilt into place and are balanced by springs inside the jamb liners.
You pull out the old sashes and stops. You remove any springs, ropes and weights that operated the old sashes. You can fill the old weight pocket with insulation.
A variation on a complete window insert unit is a system that comes with two double-hung sashes and detached tracks. Like a complete insert, these fit INSIDE the jambs of an existing double-hung window. 
The new sashes will tilt into place and are balanced by springs inside the jamb liners. 
