Yeah, it may be harder if you're a foreigner. I'm a foreigner and I managed to do it, though. If you have the cash I don't think landlords would care.
For me, the biggest hurdle was saving up the deposit. Koreans have easy access to cheonsae loans at 2-4% interest rates. It's very difficult for foreigners to get a loan in Korea.
If I was going to live in a Major city anywhere,Seoul would be in the top 2 along with Tokyo