Well not often but I have heard horror stories.
Like if someone knows your IP, is it easy for someone to get a keylogger on your computer without you knowing?
If you keep your system updated and dont directly download malware it is very difficult or expensive to break into it. It would require the use of what is called 0-day. An exploit that is not fixed and was sold in secret. This is not something your average attack has available.
I don't ever run anything. I just browse and rarely even save a picture.
I just want to know if cold storage or multisig is more secure?
There is no easy answer to this, because it depends. Multisig can be more secure depending on the circumstances. Who can sign along with you? If its you on a different computer, how secure is that computer in comparison to one that is never online?
I get that cold storage is keeping btc on an offline computer but can it be compromised at some point if I decide to spend the coins?
It can, but its even more difficult than attacking a well updated and clean computer.
Whats cold storrage? You have an online computer that shows you your balance, but has no private keys. You use this computer to create an unsigned transaction. You transfer this unsigned transaction to the offline computer. This is where it could break apart. E.g. if your online computer has malware that spreads via USB sticks and you use an USB-stick to get the TX from the online to the offline machine, chances are its compromised. The malware will have problems getting any data out though. You could also just transfer the data by hand, e.g. type on your offline system what you see on your online system. Once the TX is on the offline system you load it into the wallet software, check if its what you want, sign it and transfer it back to the online system. The online system is used to broadcast the signed TX to the network.