Just going off what I see from a Katana, it looks like something better for unarmored and/or horseback fighting, but at the same time I've seen all kinds of, at least Japanese inspired, armors. Were these made out of something really flimsy, or did they use something else entirely, or did they use their swords in a way I'm not seeing right?
Take a look at this thread for more detail.
The gist of the story is that the katana in war was primarily a sidearm, like the a late medieval knight's sword. In the Kamakura period the samurai's main weapon was the bow, while in the Sengoku it was the spear, with the Muromachi being a transition period. The Katana became the main weapon only when it became ritualized in the Edo when there were no more wars to fight.
Armor itself was first made out of metal scales laced together. It then became lamellar, or metal plates laced together. The plates became steadily larger and the lacing steadily sparcer. By mid-Sengoku, a popular form of armor appeared with the metal plates riveted to cloth and each other instead of laced. When using these kinds of armor, as time wore on and more protection was desired (especially with the spread of the arquebus) more layers of plates were added. By the late Sengoku, the richest warriors imported European style plate cuirass, or had imitations made. The limbs armor though continued to be lamellar.
Samurai 1550 - 1600 by Anthoy J Bryant, 1994