That’s pretty! I guess my answer would be no, but you didn’t know it.
A friend of mine has an aphorism that comes close to the same idea: “A sufficiently gilded cage is indistinguishable from freedom.”
I thought that freedom was just another name for nothing left to lose. 
Oops! Replace “name” with “word”.
And then there was the dyslexic atheist who didn’t believe in his dog.
Seems like many of the previous responses are talking about the nature of “free will.” And that’s a reasonable way to tackle the issue. You have to define the terms in order to tackle the question. By definition, can free will apply to non-humans, etc.
But one can also look at the issue as a developmental progression. Where in the evolutionary process (or even in the intellectual development of any single individual from infant to adult) does one begin to have free will?
IOW, to answer the OP:
Speaking very generally, I’ve heard it said that an adult dog is said to be roughly at the intellectual level of a two-year-old human child. So re-phrase the question: At what point does a human child have free will?
It makes the question more grasp-able, since we can all remember being children. To the extent that our free will was limited as children, what drove our moment-to-moment decisions and responses? Answer–self-interest and ad-hoc reaction to the world around us. Simply living in the moment.
That would depend if they are burying the bone prior to or immediately after the here and now.
That’s OK, he wasn’t troubled by the question of whether Santa existed either.
The one I remember: Person A gets told “This taxi only goes to Chicago,” and replies “Great, that’s where I wanted to go”; meanwhile, Person B gets in another taxi, and is told “I’ll take you anywhere but Chicago,” and replies “But that’s where I want to go.”
Free will is not a religious idea, but a philosophical one. Yes, religion and philosophy really are ultimately the same thing, but, as far as they are distinguished, free will has been considered in what we call philosophy well before it was considered in religion.
As for the answer to the OP’s question: you have to define free will first. Then the answer either becomes apparent or requires more testing of how dogs actually think.
Actually, it’s not a specifically religious idea, it’s an idea that may have specific religious interpretations, and religious people may have speculated about it (much as non-religious people may have done).
For me, free will may or may not be an illusion. But even if free will is an illusion, the illusion is so close to real that for all practical purposes, you could say that we do have free will. In other words, it’s impossible to do an experiment that would demonstrate free will or a lack of free will, so for all practical purposes, you may as well claim free will or a lack of free will, as you choose.
In other words, it’s an unanswerable question. A friend used to call such speculation ‘mental masturbation’. He would usually be full of crap, but in this one case, I have to agree with him.
Religion is philosophy which claims that the answers are in back of the book.
Typically in that set up of combined forces, they are stating 1 - Free Will is itself an illusion, that the existence of some constraints in choice by limited options is not the issue, the issue is that every thought is, at the most basic level, deterministic via biochemistry, we just aren’t informed enough to understand all those underlying details.
It’s one of Scott Adam’s ongoing themes on his blog. (Scott Adams, the creator of Dilbert.)
There is some argument that limited choices means you aren’t really free, but that is a separate debate topic that is not really tied to the “Free Will” argument.
You really need to define your terms. Dogs can sense their environment and respond to stimuli. They have emotions, they respond to cues from their humans, they can sense our moods and respond to them. They choose their behaviors based upon their desires at the time. They can anticipate our behaviors based upon observing patterns of behavior. They can understand words, they have vocal distinctions - different barks and growls.
That is a curious definition. I suppose you’re tying that in to the religious argument over the problem of evil and the Tree of Knowledge of Good and Evil or some such. I think most people discussing the topic are speaking in a more broad sense of whether decisions are deterministic or not.
If you want to go off on a tangent of whether knowing the choice is good or evil before you decide is relevant, then start a thread in GD. I’m sure there’s plenty of room to discuss if God was justified in punishing Adam and Eve for eating of the Tree of Knowledge of Good and Evil when they didn’t understand the moral choice, so could not be responsible. In fact, that is often the only justification for punishing humanity - because God said so. But let’s not do it in this thread.
Or maybe it is related, but the point is that they are very similar in development to children, and in fact are often more obedient and more intelligent than the same age-appropriate children.
I love it.
[Pink Floyd]Did you exchange, a walk on part in the war, for a lead role in a cage.[/Pink Floyd.
[Me]: Um, is it a gilded cage? [/Me]
Well, I don’t feel qualified (or drunk enough) to weigh in with any real authority vis a vis the philosophical implications of Free Will, I wanted to share an article I read about a recent study.
The study examined how dogs reacted to people who rebuffed their owner. Contrary to self-interest, the dogs showed a tendency to ignore the offer of food from a person who was “mean” to their owner.
This could be written off as …I don’t know…instinctual pack solidarity, but it’s tempting to say that this is a result of the dogs thinking and making emotional and/or moral decisions. It’s likely that this is simply a response to the reactions of the owners, but again, their choices were made against their own immediate self interest.
This doesnt really add anything to the discussion of free will, unfortunately, but I wanted to share. And this is IMHO, right?
<checks forum> Yes, good. It’s not GD. 