How many who have answered this have even been to Korea? First off, dramas don't give you a clue of what people are really like, they are what peoples lives would be like if everything was idyllic.
Korean men aren't short at all, unless you're talking about the old men that grew up starving during the war years. (Younger men average about 5'9-5'10 I'd say).
When they're growing up they study from early morning to late at night at public and various private schools. It is very rare even for a highschooler to have a girlfriend, so you can imagine most are not suave even in their twenties. The culture here is that (single) women are princesses who are often immature and whiny (and obviously materialistic) and men dote on them until they have them hooked into a marriage.
Once married, most men rule here with an iron fist. He will often frequent prostitutes and massage parlors once his wife starts to bore him. While not all men do this, hitting is not at all uncommon when he can't get his point across through words.
Koreans are a passionate people when compared to other Asians, this stereotype is true. They have the bowing and the same polite veneer that the Japanese have, but they can quickly get into shouting matches or even physical fights if they felt that they have been caused to 'lose face'. While the Japanese and Thais for example are also concerned with losing face, they will often withold their emotions (in public) when their pride has been violated.
This passion does carry over into romance at least in the early stages for Korean men. They behave in ways that would be considered desperate in the west, calling on the cellphone 10x a day or more, sending numerous bouquets of flowers to love interests before she has shown any true interest back to him.
They also love drinking an alcohol somewhat similar to vodka called soju. They may often work a 12 or 14 hour day, and then spend hours with their boss drinking several bottles of soju along with a fatty meat that they (and many foreigners here as well) tend to like. This is an oft occurence, so you can imagine that the home life is limited.
Sorry to burst the bubbles of you Filipino and Thai women who watch the dramas, but Korean men are not something to be sought after, unless you want a brief fling. I'm American and I wouldn't go saying American men are so wonderful, but compared to a Korean man they'd definitely be the lesser of two evils.