Is free will possible in a deterministic universe?

[iceaura]

In every possible (from subjective viewpoint due to lack of knowledge) future the dog in the example will, in that future, be dead.

In the objective possible - that aspect of the universe in which lack of knowledge is set in stone - the dog may or may not be dead, depending on which future is going to have been chosen by whatever beings in that universe have the relevant capabilities.

We can talk of what we think are possible, that perception of possibility due to our lack of knowledge,

In the case of chaos, Heisenberg uncertainty, quantum uncertainty, and so forth, lack of knowledge does not govern our perceptions - it's better and deeper and more accurate knowledge that tells us what the possibilities are, and better/deeper/more extensive knowledge that tells us what capabilities the active decision makers possess.

That lack of knowledge is set in stone, in many situations, is of course part of the explanation for the existence - the necessary existence - of mutually exclusive capabilities in decision makers.

No such possibility actually exists, if it is perceived to exist.
In a deterministic system, all future states are equally already rolled, due to the nature of determinism itself.

That conflicts with the meaning of the word "already".
It also uses a misleading euphemism for "supernatural": "actually". In a natural universe, a deterministic one, many possibilities actually exist at any given moment - one can observe them, contrast them with the capabilities that are the relevant matter here, put a number on the odds of their future occurrence, etc.

Every state of the system is wholly determined by the previous state, which means that every future state is equally wholly determined by any previous state.

True in abstract, but that involves expanding the concept of "state" beyond our current comprehensions - in time, in space, and in logical complexity.

The past moment determines the present moment, and the present wholly determines the future.
For a deterministic system this is true at all moments of time since any initial conditions.

True, but irrelevant.
The topic remains - how much and what kinds of freedom of will are among the properties or aspects of those moments?

There is no consideration of "when" - the state of the system at any point in the past is equally sufficient to determine every point in the future.

There is a complication: many physical properties are not determined at a point. They require an interval - in both space and time. The question of how long an interval of time and extent of space is required to determine - say - the phase, length, and velocity, of certain kinds of combinations of waves, comes up unanswered.