Many online poker sites where you want to play are normally not made for Linux. There are only one or two poker sites that provide downloadable Linux poker software. But it's rare. Most of the times, you will either need to wait for a long time for the poker software to download on Linux or you will never see the poker client appearing at this operating system.
When you do install the poker software, you need to fix the things up a little differently. Many people can install Windows poker games to Linux but it requires lots of technical knowledge. It's possible. It's very difficult to do for the common user.
Sometimes, the graphics cards of Linux do not work at all. Some poker sites don't give their driver details for the Linux operating system. Thus, you need to tolerate the poor performance of the poker software meaning that the poker games won't be as smooth as they could be when running on Windows.
Although when you get the Windows game working on Linux, many times you are required to tweak it or wait for fixes before the game will start again when there are major patches to the game. This is very annoying because you have to wait until a fix is made repeatedly.
And finally, if you things work well, you won't have support in case of a problem. You need to cope with on those problems on your own. Many people who play poker on Linux this way hope these kinds of problems but it's yet a huge drawback.