Since we're talking about poetry, the easy answer is of course it could. Of course, because it's poetry it might not.
A more literal reading is that our narrator is simply appreciating the beauty of the world around him on this, "the darkest evening of the year." On this journey he is observing his surroundings, and the woods are simply an integral part of what he sees. He draws us in to this winter scene and we are not in the least surprised by this description.
A more figurative reading is that the woods represent the narrator's intent to ride into the woods, never to come back. If so, the death must be considered suicide rather than the natural ending of a life. Finding certainty about this intent is probably not possible.
Because Frost is generally a symbolic writer, it's not surprising to have this kind of debate surrounding his work and specifically around phrases like this. Part of the beauty of poetry is the opportunity for readers to explore and interpret--within reason--the language and imagery of the work.
I would humbly posit my strong diagreement with the answer posted regarding the point that the narrator's intent is to stay back forever in the woods. Whether the woods represent death or not is another question, but there is no evidence in the text that supports this point. Rather, on the contrary, the poet-narrator says--"But I have promises to keep/And miles to go before I sleep". There is no intent at all to remain within the beautiful stasis of the dark woods. However much it may allure, the spirit of life is always in quest, in movement, in ceaseless struggle and in discharge of different kinds of duties, both material and metaphysical through this dynamism.
The dark and deep forest, made by someone known, yet unnamed is indeed evocative of the entire binary schema of life and death. It combines the delectable and the eerie in nature. It has its mystical lure and wants to attract the traveller into stasis while the spirit of life urges the traveller forward in an endless journey of exploration beyond this binary of life and death, into the realm of the metaphysical and transcendental, as it were.