I've recently read somewhere (can't remember the source) that multisig often doesn't provide more security in hot wallets, but increases the size and thus the fee.
I can't seem to comprehend how this can be valid (multisig not providing better security for hot wallets), what could be the reason behind this statement?
Multisig scriptpubkeys do increase the overall size of the transaction. This is because when redeeming the output sent to the multisig script, a number (typically larger than one) of signatures have to be provided for validation in the redeeming transaction.
As for security in multisig, it depends on the setup of keys, and the scriptpubkey that ends up being executed. For example, for a 2-of-2 multisig script (where two signers must cooperate), it might seem that this script is "more secure" against an attacker obtaining one of the keys, but if both keys are kept on the same device, then there is no security to be gained from a multisig.
On the other hand, if the script is a 1-of-2 multisig, then even if one of the keys is highly secured but the second is not, then the security in having a second signer (secured) is subverted.
Bitcoin's scriptpubkeys can be programmed to require not just multiple signers, but also conditions on when these multiple signers should participate or when they shouldn't. We could set up a 2-of-3 (requires at least 2 of the 3 predetermined signers to participate) multisig scriptpubkey such that :
In normal operation, the low security and medium security signers will cooperate to sign the user's transactions. The user can rest easy knowing that even if their low security key is obtained by an attacker, the funds will remain safe. The attacker will need to obtain the medium security key (the one that belongs to the 3rd party service) as well to actually move the funds. If the service itself disappears, the user can still make use of their high security, cold storage key to complete the script with two signers, so they are never "locked out" of their funds.
There are even more ways to upgrade this setup, using ntimelocked transactions, or encoding a lock time in the script itself using op_csv or op_cltv.
I believe Greenaddress is using a setup very close to this.
So to answer your question, multisig is just a tool. The security (or not) gained by using this tool depends on the way that it is used.
Using a hot wallet multisig can be more secure than a singlesig hot wallet, provided that you do it right. For example, you segregate the keys on separate devices which are kept in separate locations and you require multiple signatures for spending. Hot wallets are inherently less secure but a well-executed hot wallet multisig has benefits just as a well-executed cold storage multisig has benefits over a singlesig hardware setup.
Of course, most individuals looking into multisig are going to be interested in doing it with hardware devices because people typically upgrade their security by moving from an exchange to a hot wallet to a hardware wallet to a multisig setup. In a group setting, however, a company with numerous employees requiring a fairly large quorom for a spend may be interested in hot multisig because of the physical segregation involved in, for example, multiple company executives having keys on their respective cell phones or laptops. Each hot device is a risk but the risk that one attacker will compromise numerous hot devices is much lower.
With regards to the addition fees invovled in multisig, multisig transactions are more expensive because they require additional signatures, which increases the size of the transaction. Nodes have to store the transaction data and you have to pay more for more storage. You pay more fees for more real estate.
