Hi there. I'm usually more of a lurker but this question caught me and I was just thinking about similar things. I'm 8 months on T and my skin and hair have largely remained of a good texture with some research. I find that T will make your hair coarser just as a matter of things, but it can be stemmed off with a change in products. I read the labels on the new shampoos and soaps I was buying out of the mens section and found that there are some important differences between them and womens soaps. They seem to have more of a detergent/deodorizing quality whereas womens or neutral things tend to have more dimethicone, a softening agent. Another thing mens products encourage is to use one soap for everything, or using a 2 in 1 instead of separate shampoo and conditioner. I grew up in salons owned by family members and I remember this being told to me as a distinctly bad thing to do. Stripping the oils from your hair, especially without using a conditioner to replace them, can gradually dry your hair out and make it frizzy, rough, and unmanageable.
To soften your hair back up, definitely watch what kind of shampoo you are using and don't skip the conditioner. For shampoo, find one that is geared towards dry hair. If scent is a concern look for a neutral brand. I actually like Suave's "smooth" shampoo. Even the shampoo has dimethicone in it too, not just the conditioner, so that's like two shots of lotion for the hair. Leave the conditioner on your hair for a minute or two before rinsing for maximum effect. If you need even more conditioning, look for a hair mask to be left on after conditioning that contains something like egg whites, honey, barley hops, avocado oil, olive oil, etc. If your hair is still dry after that, a spray-in conditioner or detangler may help. John Freida makes some very good defrizzing products. Stay away from gels and hairsprays if you can. They can both contain alcohol, which will destroy your hair in short order especially when combined with use of a hairdryer. Instead, look for waxes, especially those based in water (for light hold) or beeswax (for stronger hold) if you're doing the spike thing.
If rough body hair is also a concern, but you don't want to fool around with applying lotion outside of the shower... I like applying it in the shower and rinsing it off. No sitting around greasy waiting for it to absorb and it still gets the job done because your pores are open from the shower's warmth. Again, the ingredients of the lotion are key here. Nut oils like sunflower, soy, shea, coconut etc. are best. Look out for lanolin and petroleum - gunky and potentially pore-clogging, which is bad news for those of us with acne from T. Sunflower oil can even help to get rid of acne.
Hope that helped.