First of all, wormholes are not the same as closed timelike curves (time loops). Wormholes are a way to connect two spacetime regions that would otherwise be separated. Wormhole may link two different universes or two distant regions of the same universe at the approximately the same moment in time. Such structures would not necessarily cause any of the paradoxes associated with time travel.
Even if wormhole connects regions of the same universe at different times in a way that corresponds to time travel (when we can say that closed timelike curves are formed), formation of such curves does not mean that there would be any material object traveling along one. There may not be any object (or being) for which its future is its past, just that future has a potential to influence past, and that influence is exercised in accordance to ordinary laws of physics.
So if time-traveling wormholes are at all possible, then there should be nothing special in traveling through one (at least in comparison with travel through wormholes connecting distant regions of space).
There are many models of wormholes so the answer to what would be the experience of someone traveling through one depends on the model chosen. One model is Reissner-Nordström black hole. Observer who falls into such a black hole can emerge in another universe. For visualizations of such a journey I recommend Andrew Hamilton webpage. Note, that inner Reissner-Nordström geometry is unstable, or quoting A. Hamilton:
Warning: If you fall into a black hole, you will die. You will not go through a wormhole to another time and place.
Another class of wormhole models is by Matt Visser:
- Visser, M. (1989). Traversable wormholes: Some simple examples. Physical Review D, 39(10), 3182, arXiv version.
This is most closely resembles sci-fi tech: traveling through one could be as simple as walking through the doorway without anything noticeable happening during the crossing.