The sap should not be a problem. I've cut quite a bit of White Pine and Red Pine over the years and the sap does not come out of the wood really until after you saw the log into lumber. I am suspecting too that the sap has not completely come up from the roots yet so the tree might still be waking up form its dormancy. Of course that depends on where you live. Here, we are still snowmobiling!!
If you are a clean freak like me and like to keep your saw clean and shiny, I found that washing and waxing the plastic keeps the saw from getting gummed up with sap. It sounds sissy like, but I take care of all my stuff and when I was logger, I especially took care of my chainsaw. Once a week I washed and waxed my saw and that was 15 years ago. The saw still runs and looks sharp to boot.
Of course on here, if there are no pictures then it didn't happen so I will leave you with one. The first one is of a Basswood Tree however, and I am using a bulldozer instead of a skidder, but trust me I cut my share of pine too as can be seen in the next, but smaller, picture.
I have no intention of traveling from birth to the grave in a manicured and well preserved body; but rather I will skid in sideways, totally beat up, completely worn out, utterly exhausted and jump off my tractor and loudly yell, "Wow, this is what it took to feed a nation!"