Yes although you may not notice sap oozing out of trees all year round the tree constantly has sap inside it and is constantly producing new sap.
Sap is like blood for the trees.
Our blood carries oxygen and nutrients to our bodies and is very vital for us to live.
The sap is the same way for the tree as the sap in a tree carries important nutrients, water and hormones through the tree that are essential for a healthy tree.
When you prune a tree sometimes you'll notice that it drips sap which is the blood for a tree and pine trees may ooze the sap out all year long while some other trees may only ooze the sap out when it becomes fall or winter.