Having your own router for untrusted networks is actually a good idea to protect your other devices. By default, any current version of OpenWrt (18.06.8, 19.07.3) should be up-to-date with security patches and the default firewall will protect the device itself as well as your 'downstream' clients. Being on a public network (hotel, cafe, etc.) is no different than being on a normal public IP address on the internet (say at your home). The protection offered by a firewall (and the slight obscurity offered by NAT for IPv4) is generally recommended when it is an option and practical. Having your own travel router also has the benefit of a consistent, private, and secure network to which your devices connect and share resources. For example, you can have a laptop, tablet and phone connected without having to configure individually every time you go to a new location -- just update the connection to the internet on your travel router and you're good to go (check out TravelMate).
You can optionally add VPN connectivity to your OpenWrt travel router so that all traffic from your router is encrypted between your network and the other VPN endpoint (commercial or your own VPN somewhere).