Yes, they used field telephones. Early in the War they used the EE-8, which was replaced at some point ( I am not precisely sure) by the smaller and lighter TA-312. If there was a temporary location ( like a forward position) light wire might be strung to it, but for someplace that was going to stay put for a while, heavier wire was used. The difference was the light wire could be laid by a couple of soldiers with a small reel, the heavy stuff might be put down by a heavy reel mounted on a truck. There were also all the components need to make a network, so not only could those field phones be used point-to-point to connect two artillery emplacements, but they could be linked up with a switchboard to make up communications for the camp- ergo Radar O'Reilly. Although it would be possible to lay a new phone line from the MASH to Seoul ( there would have to be a repeater, something to boost the signal, about every 20 miles) and perhaps such a thing did exist, it was possible to patch the phone network into existing telephone lines. Of course radios would also be used, but the phones took much less current and were better long-term. The camp radio would need a gas-powered generator running to power it, a radio emplacement out in the field might need a soldier cranking away on a generator to do the same thing, and the AN/PRC-6 "walkie-talkie" handheld radio would have only a range of a mile and a battery life of 4 hours.

If you liked the TV series, EE-8 and TA-312 phones were made in huge quantities, and later were dumped into the Civil Defense system. So, you can still find them, field wire, parts and sometimes even switchboards for sale. The TA-312 take standard D-cell batteries, and are easy to make into an intercom system.