Do I need to forward a port on my router to run a node?

No, port forwarding is optional. A node that only makes outbound connections is still fully validating and perfectly useful to you. Forwarding the node port lets your node also accept inbound connections, which helps the wider network because new nodes can connect to you while they bootstrap. If you want to be reachable from outside, reserve a fixed local IP for the node machine and forward its listening port at the router, then allow it in any local firewall. If you skip this, your node still works fine; it just will not host new arrivals.