Smoking chicken breasts with and without skin
It's not a question of fat.

Tougher meat- that is, meat with more connective tissue- needs to be cooked low and slow to melt out that collagen and make the meat fall-apart-delicious.

Meat with little connective tissue does not benefit from low and slow.

Ribs, pork butt, and brisket are cheap (they used to be anyway), tough, pieces of meat. Smoking them at low temperatures for a long time fills them full of flavor and dissolves their collagen, making the delicious BBQ we love. You don't want to smoke these at higher temperatures because the proteins will be fully cooked before the collagen has melted.

Poultry doesn't have as much connective tissue. The only purpose in smoking it is to impart the smoked flavor. The faster it reaches its target temperature the less time it will have to dry out and the more moist it will be.

In either case- overcooking will yield dry meat.

Some tips for moister chicken:


Always cook chicken at higher heat so it cooks faster.
Use a thermometer and take the chicken out when the white meat is around 160F. Overcooked proteins squeeze out moisture and the extra cooking time dries it out further.
If your smoker doesn't get hot enough for fast cooking (mine doesn't) smoke the meat for 20 minutes and finish in the oven or on a grill. It will absorb almost all the smoke it is going to in that time.
Brine the chicken. Wet or Dry brine recipes work. I prefer dry brining. There are many recipes online for how to brine. The added salt super charges the meat with water and locks it up even after cooking. It takes some planning ahead but makes a huge difference in moisture.
Chicken smoked with no skin will dry out on the surface. There is just too much air moving around. On the other hand, the meat itself will absorb the smokey flavor instead of the skin and fat. It's a tradeoff. Even if the surface is dry the interior of the meat can stay moist if it doesn't cook too long.
Increase the surface area of the chicken to decrease the cooking time further. Cutting meat lengthwise to fold it open is called "butterflying". It works best with whole birds but can be done with breasts.




In general, I find that smoking is best done with whole chickens. Breasts just cook too fast. I think you will enjoy you smoker more if you brine and butterfly a whole roasting chicken and save the skinless breasts for faster cooking methods.