Dormant Oil Spraying
Usually right around the time your pruning it's also a perfect time to do dormant oil spraying. Ideally do your pruning first, you'll use less spray, your tree will be more open and you can spray all those new cuts you made to keep anything out of them.
Choose a nice warm sunny day. This will allow the spray to dry and coat the tree better. Avoid spraying if it's going to rain in the next day or two as it will just wash off, and avoid high winds as it will be harder to control.
The reason to spray is to control any harmful insects and there eggs that may be harboring on your trees over the winter.
Recently I've been using a larger volume back-pack type sprayer and this thing is a dream, but I also have probably 20 pretty large trees I'm spraying. You can probably get buy just fine with a simple pump type with a hand spraying wand if you have a few trees.It can be a bit awkward to carry and spray higher into the trees and I felt I was constantly pumping it. I definitely should have upgraded sooner and if your avoiding spraying cause you hate your pump sprayer (like I did) then get the backpack.
Another tip is to be sure to clean it well and spray some water through when your done or it can get pretty clogged up and messy. (and when you do dismantle it too clean it, find a nice clean space (not in the grass of the orchard) it seams to have a a lot of tiny pieces that like to spring and launch away).
The Dormant Oil
So the "dormant oil" isn't actually one specific thing. You are spraying the "dormant" tree with "oil". Don't get me wrong you can go to the hardware store and buy "dormant oil" like the one below. But it's a mix of lime sulfur and horticultural oil, you mix with water and spray. The lime sulfur can give you a bit of added fungicidal coverage than just using an oil based spray, but then it is a chemical you are adding to your garden. I'm not going to open the debate on that.
If you prefer you can also make your own simply with 1 cup vegetable oil, 2 tablespoons of dish soap and 1 gallon of water and mix it well in your sprayer. There are all kinds of other concoctions that include peroxide or baking soda and different people recommend different types or soap and oils. Feel free to do a quick google search of your other options.
Whatever you prefer to use I do strongly recommend spraying with something, especially as you start getting more trees. Don't underestimate how fast a pest or fungal problem can get out of hand and how devastating it can be, and this simple prevention step is strongly encouraged.