Sparrow is not a web wallet, but it is a software wallet you download. If you use bitcoin you need to use Sparrow Wallet.
And yes it is a hot wallet, but since you have a passphrase on your seed words and your passpharse is never stored on a computer then I think that can be said to be a "cold" wallet.
However, a hardware wallet keeps your seed words off a computer completely (only stored on the device) and you need to have it to sign for transfer of the UTXOs, thus that is said to be truly a cold wallet.
