This is a really difficult question to answer - you're asking students of the past to look into the minds of people who are no longer around, and who, in large part, didn't really leave much record about their personal feelings on the subject. That being said, there are a few journals from the time period in question that might help you out.
Check out the journal from Private Joseph Plumb Martin. He was enlisted and was present at several of the more well-known engagements of the American Revolution. His journal has been published several times. I recommend this version: http://www.amazon.com/Private-Yankee-Doodle-George-Scheer/dp/0915992108/ref=pd_sim_sbs_b_1?ie=UTF8&refRID=0M5DEH4JEF3BP72EKMSH
Martin is a most interesting author, as he doesn't hesitate to tell his audience about how he really feels regarding the war, and his part in it.
There was also a journal written by a doctor who attended some soldiers at Valley Forge - Dr. Albigence Waldo. A link to some of his excerpts can be found here: http://www.let.rug.nl/usa/documents/1776-1785/albigence-waldo-from-the-diary-of-a-surgeon-at-valley-forge-1777.php
It is from Dr. Waldo's account that we tend to extrapolate the stereotypical idea of the starving, bloody-footprints-in-the-snow suffering of the typical enlisted soldier at Valley Forge, but in my opinion, the scene was much more complicated than that.
It was a hard winter, yes. Were the men just waiting around to starve and die? No. A fair number of enlistments were expiring at the time, so one answer you may have gotten would simply have been "freedom for my home, but my time's almost up here, so really, nothing. I'm going home."
It was at Valley Forge that the soldiers of a variety of ranks learned how to be a standing, "Regular" army - fashioned after the best one in the world at the time. Guess who that was? You're right - the British. It was under the tutelage of the Baron von Steuben, interestingly enough a digraced Prussian officer, that these ranks became a true fighting force. I will say though, that you might've been hard-pressed to find and officers of higher rank than field officer at Valley Forge. This had a serious impact on how the various regiments were provided for, how they conducted themselves in camp, and how their overall accommodations panned out.
For example, General Wayne from Pennsylvania had his 2nd regiment in tow - called "Mad Anthony" Wayne, since he was actually in residence at the encampment, we see some startling things. His men had the best rations, all of the supplies they needed, and were hutted up in strict regimental rows. General Wayne was on hand to personally see the Quartermaster and to fight for anything they might need. Please understand - the Quartermaster's office was in shambles at this time - it was impossible to get anyone to take on the title, and they never stayed long. Congress was so preoccupied running away from the British Army, it's no wonder they had little time to see to the actual material needs of the Continental Army. If you asked on of the 2nd PA, they might tell you they are fighting for their homes, their brothers, and their General.
By contrast, we know that the Virginia brigades didn't have any generals present at the encampment. They were poorly supplied, and when examining the archaeological evidence, we see that their huts were actually all constructed willy-nilly (yes, that's a technical term). They didn't adhere to regimental roads or a formal encampment layout, right down to the varying sizes of their huts, and where the fireplaces were located in those huts. We see similar disorganization among the ranks of General Varnum's Rhode Island brigades on the north side of the encampment.
Perhaps if you asked a VA or RI regimental soldier what they were fighting for, their answer might have been different from those of the PA brigades.
Interstingly enough, another thing we see on the fringes of the Rhode Island brigades are the production of USA buttons. The ones that everyone knows about are actually from the very end of the war, around the 1781 time period. They look like this: http://www.pinterest.com/pin/473370610804329538/ (sorry for the pinterest link, but it's a perfect image)
What a lot of people don't know, is that during the 1777-1778 winter at Valley Forge, they were producing the predecessor to that button. The predecessor was dated 1777, and looks like this: http://www.kellycodetectors.com/treasure-stories/1777-usa-continental-army-general-service-enlisted-soldiers
This one was found on a CT farm by a metal detector.
Source for that info: Me. There are about 4 of these known, and it was my archaeological excavation at Valley Forge that dug up 2 of them. The one you're looking at is the same as the one that is found pictured in Don Troiani's book "Military Buttons of the American Revolution". The two I excavated are the same - one is fragmentary (only a third of the button survives), and the other is a miscast. Find Troiani's book here: http://www.amazon.com/Military-Buttons-American-Revolution-Troiani/dp/1577470613
It's interesting that the men of the Continental Army started removing their regimental buttons at Valley Forge (we found 3 buttons of the 2nd PA regiment waaaaaay far away from the PA's encampment, in the RI brigades' space), in order to make way for the USA button. USA= United States Army. Washington issued a general order eventually, stating that each man no longer fought for his own colony or regiment, that instead, he was now fighting for the United States Army - the collective Continental Force that would eventually face down the British, and show them just how little will they had to hold onto so non-lucrative a set of provinces.
If you asked the guys making or sewing on these buttons, I imagine their responses might have been different again.
And we can't forget that Valley Forge saw one of the first instances of soldiers of African descent (all free men) fighting for a cause. Just imagine what their reasons would have been for fighting. There is a monument at Valley Forge dedicated to these men, too, who fought for a country that only marginally (if at all really) recognized them as free, complete, equal citizens.
There's a lot to your question, simple as it may seem. A lot of men left the army at Valley Forge, many were sick. It was said that 1/3 of the army was not fit for fighting at the time of the march-in on December 19, 1777. Imagine if the British had simply tried to take the encampment. They wouldn't have failed. But Howe and his army were content to pass the winter in the relative warmth and comfort of the loyalist homes of Philadelphia, allowing the Continental Army under Von Steuben to become an actual, formidable fighting force. They needed practice of course, and lost many battles thereafter...but I wouldn't be surprised if polling soldiers at Valley Forge would've resulted in an increased resolve from all present to maintain their dedication to the cause of Liberty (yes, capital L), which allegedly brought the majority of them from their homes in the first place.
If you are interested in Valley Forge, definitely check out the following books, and if you have any questions about my personal work, do feel free to PM me.
The Valley Forge Winter: http://www.amazon.com/Valley-Forge-Winter-Civilians-Soldiers/dp/0271025263/ref=sr_1_1?s=books&ie=UTF8&qid=1404440440&sr=1-1&keywords=Valley+Forge+Winter
The Drillmaster of Valley Forge: http://www.amazon.com/Drillmaster-Valley-Forge-Steuben-American/dp/0061451649/ref=sr_1_5?s=books&ie=UTF8&qid=1404440463&sr=1-5&keywords=Valley+Forge
The Philadelphia Campaign, Volume 1: http://www.amazon.com/Philadelphia-Campaign-One-Brandywine-Fall/dp/0811701786/ref=sr_1_2?s=books&ie=UTF8&qid=1404440482&sr=1-2&keywords=The+Philadelphia+Campaign
The Philadelphia Campaign, Volume 2: http://www.amazon.com/Philadelphia-Campaign-Germantown-Roads-Valley/dp/0811702065/ref=sr_1_1?s=books&ie=UTF8&qid=1404440482&sr=1-1&keywords=The+Philadelphia+Campaign
Just for your information, my training is in Fields of Conflict Archaeology, with a particular concentration on the American Revolution. My doctoral dissertation focuses on the winter encampment of 1777-1778 at Valley Forge.