Alpine used different fluids for the hydraulic system over the years.
We also have a 2003 38'. Our owners manual states Dexron and when I recently changed the filters, that is what came out and went back in.
Hopefully if someone else with a 2003 has a label showing a different fluid they will chime in.
BTW, here is the number of the filters (3 of them):Wix 57317
Unless there is a problem with contamination (unlikely unless a component fails, as this is a sealed system) I just remove the lid, siphon out the oil fluid, then and only then remove the wing nut, washer and filters. This way you are not mixing the unfiltered (outside the filters) fluid with the filtered fluid.
Replace the filters and refill with fluid.