Those Pesky Buttons
Most children are able to learn buttoning one-handed, albeit a year or two later developmentally than when most kids button. I believe that this is the most effective method available.

Of course there are many adaptive devices which are designed for one handed buttoning, all of which work adequately, but I find that most people like to button one handed instead (except for that last pesky button on the sleeve for the unaffected arm). The best place to see all of the options is in the Sammons/Preston catalog, which most OT or PT departments will have.

Lastly, there is always the option of modifying the clothing with velcro or some other fasteners.

Mittens
Polar fleece mittens that fasten with velcro are useful. Gymboree and Gap Kids carry these.

It is often times very difficult to keep a mitten on the affected hand. Many mittens are lost as they fall off when the child is playing outside and buried in the snow somewhere, to reappear in the spring. The ones that snap to the coat are often to difficult for our children to reattach, using yarn and crocheting a single strand and then sewing it to the mittens make sure this doesn't happen. This then strings through the coat. It can also be tightened before the coat is put on and this helps keep the mitten in the coat sleeve while playing outside. You will have to loosen it though once done, so they are able to get the mitten off and on while at school.

Putting on a Coat
From Amanda:
My son was taught to put his coat/cardigan/jacket on the floor inside up with the collar facing him. Then he reaches down to put both arms through the sleeve holes at once and lifts it up over his head. It is great to help him try to stretch his left arm by himself while at the same time allows him to use both arms simultaneously. I don't know about any of your children but Jake seems to be able to achieve a lot of maneuvers with his affected left limb if he does the same action with his unaffected right limb at the same time. (a kind of mirroring)

He first learned the coat technique when he was about two and a bit and it gave him such enormous pleasure that he was independent in this way and could put a coat on like his peers. Hope the coat trick helps.