Can you explain what you mean by "connecting your Trezor to Electrum"?
Do you mean when sending to and from Electrum? Do you mean viewing your coins in some way?
You can use Electrum to access you Trezor wallet's and accounts, but only the Bitcoin accounts. There are Electrum forks for other coins, but I don't want to confuse the issue. To access your Trezor with Electrum you'll need to have your Trezor connected to the PC you're using, and create a new wallet in Electrum. It'll ask you what kind of wallet you want to create (choose "Standard,") then it'll ask if you want to create a new seed (choose "Use a hardware wallet.")
This will allow you to use Electrum to view and control the bitcoin accounts in your Trezor.
I have my coins on Electrum at the moment and am happy, but wanted to get a cold wallet for added security*
I assume you have a desktop wallet currently with Electrum, that wallet will not be affected. Using a Trezor with Electrum is still more secure than a standard desktop wallet, since you'll need to connect and unlock the Trezor to interact with the new wallet file.
[* To be honest, I have been astonished at the number of technical issues I see on their forum. I thought a cold wallet was all about just dumping your coins and forgetting about them for years? It looks like you need to check all is well every day, like a cat on hot bricks!]
A hardware wallet isn't a "cold wallet." The point of a hardware wallet is to have a wallet on a device that is isolated from your PC and mostly immune to viruses and malware. Hardware wallets are definitely more secure than a standard desktop wallet, but they are usually used for wallets that you want to interact with regularly.
Most people here will define a "cold wallet" as a wallet that was generated on an off-line PC that will not be interacted with regularly. For example; I installed an OS on an old laptop, used it to generate a seed phrase, wrote down the seed phrase and put it in a safe place. Then I formatted the hard drive on the laptop so no trace of the seed phrase is left on any electronic device. That's my cold wallet, where the majority of my coins are kept.
I use hardware wallets to house moderate amounts of bitcoin that I want to spend from time to time.