Hi!
I put my son on cows milk in the morning and formula at night because I felt that way he was getting all the goodness added to the fomula. Did this till he was about 20 months and then used up a box of formula and gave him cows milk at bedtime too. My daughter is 14 months now and on formula, and I intend to do the same with her.
Marette - I changed the morning drink to a cup first, the theory being that as they're desperate for a drink they're more likely to go with the change. Worked with both kids, but it did take a few days. What I've just done with DD is let her drink as much or little as she wanted, then use what was left to mix her cereal. Now she drinks it all. Also, she started playing with her bedtime bottle so one night last week we tried giving her the cup and she's taken to it fine! You might find that when you make the change your little one will drink slightly less in each feed. Apparently that's normal, so don't worry.
As for the constipated thing - I think that as long as they drink lots of water during the day, and eat lots of fruit and veg things should be OK. If in doubt, try Organix prune porridge - it worked wonders with William!!
Hope this helps.