I agree with Mike in that up in KS, I have found it hard to tell by just feel or visual where the dryline was. However, down south of Amarillo, it sometimes can be quite dramatic. I find often on good storm days, it gets rather windy/dusty on the back side of the dryline in the midafternoon and muggy/hazy on the front of it.
Visually, that can be seen IF you are in the vicinity of the dryline. On days where it's really sharp and you drive through it on the surface, you often instantly know. You can feel it in your breathing, sometimes the windows might briefly fog up as the air inside equalizes with the air outside. It's not unheard of to jump 50 degrees in dewpoint within a 10 mile stretch. Not entirely common, but not unheard of. As Mike says though, where the dryline meets the surface, the moisture is rather shallow.
I remember one day back in 2000 it was clear as a bell out west and there was this cloud bank to the east. Dewpoints were very low (don't recall exactly now) west of the dryline and high to the east. We went into the low, foggy cloudbank to the east which lasted about 20 miles or so aroud Matador, TX, a supercell was already in progress to the east of that which we could see above the low clouds when we were behind the dryline (got a late start that day). This was the day Olney, TX was hit by a tornado from another storm later in the day. The dryline change was very dramatic that day.