All trees should be mulched. Mulch keeps in the moisture and reduces mechanical damage from weedeaters/lawnmowers. It also allows water and nutrients to get into the root zone that the grass would otherwise use on the surface.
Mulch all trees to a diameter of at least a foot. Do not place mulch thicker then 3 inches and do not place mulch right against the trees.
If you want to do some pruning yourself, please use these guidelines: Never-ever "top" a tree, which is lopping off multiple feet because a tree is "too tall", please refer to article below. We never take more then fifteen percent of live growth off as trees already have a hard time in Colorado. Also do not leave stubs as they are unsightly and can harbor diseases. Also do not trim only the interior, this is called lion tailing. This practice causes the ends to stay heavy while not allowing the interior support branch to thicken. If you are not sure, please call a professional.
Smaller sized trees and shrubs tend to do better. They will catch up to and often pass larger size trees. They are also less expensive and easier to handle. Dig a hole at least 1.5 times as wide as the root ball or more if possible. Dig the hole as deep as the top of the plant is or maybe an inch or two shallower. Sometimes you have to find the top of the root ball as soil can be piled on the root ball and make it appear taller then it is. Mix a one-to-one ratio of existing soil to compost and hand pack this mixture around the root ball. Also it is now acceptable to not stake trees. Stakes tend to be a crutch and not allow the tree to establish strong roots. Also people can trip and/or run into the poles/wire injuring themselves. Also straps can be left on the tree and can imbed causing failure points. When you plant container trees, look for circling roots and if there is any try to break them apart.
Trees and shrubs should be watered during the winter to help combat the dry soil conditions when there has not been any moisture and the temperature is above freezing. A small trickle for about 20 minutes a side just outside the end of the branches should be adequate.
All to often we see pine trees next to the house or a big maple tree in a tiny yard. The way to combat this is too plan for the future, i.e. check the mature height but more importantly the mature width also called the spread. Remember the roots are roughly as wide as the tree is tall. Take this into consideration so driveways and sidewalks do not get damaged from roots.
Never cut off more then a third the height when you mow. Water deeply, a light trickle for longer is better then a flash flood. This forces the root system to chase the water and go deep. Also, try to plant grass that can handle our dryer conditions like a fescue. The common grass in Colorado is Kentucky Blue Grass. However it is cool season grass that thrives back east with better moisture, humidity, and soil conditions.