When my daughter was a baby, she ate everything. Now that she's two, she eats nothing aside from goldfish crackers, pasta, tofu and eggs. No vegetables. Don't they all love mashed potatoes though? Heck, who doesn't. So I chop stuff up real small, and hide it in the potatoes. And she eats it. I can even go as far as crumbling some tofu in it and making it a one dish meal.
Now, I know you can still see the green mixed in with the white - but I swear, if you chop the vegetables up really super small, then mix them in, it's fine. You really can't taste them, even though they are there. I like to use something without a strong taste, and that packs a huge nutritional punch -- my favorite is swiss chard, but spinach works too. Broccoli is hit or miss, but cauliflower is easier (although both kinda smell like farts if you ask me).
If you have a ricer, you're set. It takes only minutes. Cook the vegetable. Pop the potato in the microwave. Push it through the ricer. Add a little butter, enough broth to reach your mashed potato thickness preference, and then salt and pepper of course. Chop the cooked vegetable as tiny as you can get it and mix it in. That's it. I like to do no more than 20% vegetable in the mix. I don't want to push my luck, if you know what I mean.
Anyway ... don't take my word for it. I have photographic proof: