SnowRunner proxies requests through their own servers before passing these along to mod.io. Focus Home Interactive is aware of the issue at their end however there is no one fix and each issue will need to be diagnosed individually as there may be several different causes.
One common cause is the use of a VPN. Please disable any VPN or proxy. Custom firewall rules that block certain countries, either on your PC or router, may also be the cause.
10001 error means that the request has failed due to unknown reasons.
10005 error means the request timed out.
Having spoken to the team, they have asked that anyone facing issues with these error codes please contact their support team by opening a ticket at https://support.saber.games/hc/en-us/categories/6056441571345-SnowRunner - they will then check their logs to try and assist you with this issue.