One thing to think about blown-in insulation from outside holes is that many of the framing segments have stop-gaps halfway up the wall for fire protection or other reason. Or it could be stopped from electrical boxes. As a result, blindly-blown in insulation from the outside often does not end up filling the entire wall; it only fills the space that gets opened. Kinda like putting a blanket on just your upper body at night: your feet still get cold.

If you can afford the time and inconvenience, I would instead recommend removing the drywall, installing good insulation, and re-drywall. It sounds daunting, but I have done it and it is by far the best way to do it. Also, you can install a vapor barrier between the drywall and insulation to prevent mildew, which I presume was not done on your home if it was not insulated properly. You can also rearrange the electrical work while the walls are down, if necessary. But even if you do so just to insulate, it will give you a much sounder wall and is definitely worth the hassle.

Finally, if the home was so cheaply built so as to not use insulation, the walls you will be replacing probably are not that good, anyway. New drywall would be a vast improvement on the inside, as well.