Of course you can.
I lost 50 pounds in 6 months. You may have to go the extra mile (so to speak), but it most certainly can be done.
bac0s said some really good things.
I experienced a significant decrease in insulin requirements as I lost weight. At first, I kept getting low blood sugar reactions with intense exercise, but I figured out how to keep that at bay -- for me, eating something with protein and complex carbs + starting my workout with a blood sugar level in the 200-250 range really helped.
I also found that eating within 30 minutes of waking helped, as well as eating every 2-3 hours.
Losing weight with type 1 diabetes can be a bit difficult due to all the daily annoyances of keeping our blood sugars within a decent range. I know a bad hypo episode can throw me off plan for the entire day, and the most annoying bit about it is that I feel it's not "fair" because it's not my fault! It's easy to take too much insulin and then "feed" your insulin with extra sugar.
Here is some advice:
Make sure you test your blood sugar before working out. Eat something high in protein also, because working out will make you really, really hungry, and something high in protein or fiber will help you feel less so. Try to avoid taking more insulin than you need (which is really tough sometimes when you still want to maintain good control, I know) and of course, there is the typical common dieting knowledge of limiting your portions and not eating when you are not hungry.