For the enlightenment of those supplying the comments: in the old unix days (mid 1980s), certain ports could be queried via inetd for responses: for example, "finger" would be able to provide information about a user on a remote host. The OP of this thread is basically asking if there is a similar way that one can obtain the date/time of a remote Linux host.
Yes, in the old days there was a similar service called "daytime" provided by inetd. You need to set up an inetd or xinetd service on the host and enable this service. Then you can connect to it over tcp or udp and it will respond with the local date/time on the host.