I have an MikroTik box which routes client traffic and also multiple dedicated Squid cache servers. I want to redirect all the HTTP traffic that goes trough the MikroTik box to the Squid servers in a load balancing manner. I don't want to forward the HTTP traffic to only one Squid server, but I want a round robin forwarding. Some requests should go to Squid1, other requests should go to Squid2... and so on.

I've read in the documentation that RouterOS can be configured with a WebProxy which also supports a parrent proxy to be configured. But I haven't read anything about multiple parents. Squid supports multiple parent servers with a round-robin request distribution between the partents, for example:
cache_peer proxy1.isp.com parent 8080 round-robin no-query
cache_peer proxy2.isp.com parent 8080 round-robin no-query

Can the RouterOS WebProxy be configured in a similar way, with multiple parents?

Any other suggestions on how to load balance the HTTP traffic to all my Squid proxies?

No, is not posible. Mikrotik not use squid for proxy cache. Redirect width Mikrotik in transparent mode for 1 Squid server, then, these Squid make Round Robin or weight with others Squid.
Best Regards
Paul