I'm currently trying to transfer my bitcoin from an exchange to a cold wallet for the first time, but I'm wondering if it's safe to keep everything in one wallet from one company.
The part of the sentence which I bolded made your statement sound like it is the company that's going to be in charge of the bitcoins you keep in the wallet, I personally think you should understand that when it comes to non-custodial wallets, the company have nothing to do with how much bitcoin you decide to keep in your wallet, your coins are your coins, as long as you are in charge of your private key, you can decide to keep your bitcoin in one hard wallet or divide them across multiple hard ware wallets from different brands, it doesn't matter as long as those wallets are non-custodial.