So here’s the thing…one of the first superhero comics I remember reading was Captain America Vol 1 Issue 388, which started in media res with Captain America and his teammates plummeting to their deaths because MADAM (the female MODOK) has cut the parachutes attached to their ejector seats…and it was deep and unironic love at first sight:

So the answer to your question is that, yes, Captain America was affected by the 90s, but more in a cheesy 90s RADICAL TO THE EXTREME way than a particularly grimdark way. As a result, you did get ridiculous stuff like Capwolf:

And there was a brief period where a meth lab explosion caused a chemical reaction with the super-hero serum which meant that his body began to deteriorate so he needed a powered exoskeleton (because power armor was big in the 90s), or the time that Cap got “vibranium cancer” in a fight with the Beyonder and was accidentally cured by Klaw, and a bunch of other 90s cheese.

But that stuff is mere rococo ornamentation on top of Mark Gruenwald’s 137-issue run, which gave us Crossbones, the Serpent Society (a villain worker’s co-op complete with health benefits and profit-sharing), Diamondback (Cap’s ex-villain longtime girlfriend), Flag-Smasher (a bizarre anti-nationalist terrorist), Left-Winger and Right-Winger, Cap resigning over the cover-up of Nuke’s attack on New York which leads to a right-wing Captain being put in his place by the Commission on Superhuman Activities, which leads Cap to take up a new identity as “The Captain” (which is probably Cap’s laziest secret identity ever), which leads the two of them to fight and ultimately Cap helps out the right-wing Captain who’s losing his mind. 

As far as the rest of the 90s go, I wouldn’t bother with the Heroes Reborn arc, although Liefeld is apparently a nice guy who’s actually been working on his art in recent years and has learned to draw feet, so we shouldn’t hate on him so much.