[2020] High ping during hordes.

Your friend’s server is likely struggling to run everything during horde night. Their ping would stay low regardless, since it’s trivial for their machine to ping itself, but their performance may still suffer. Your options are to

• beef up the server. Check the game’s system requirements, noting the added requirements for a server. Perhaps you have better specs than your friend so you should be the host, or perhaps one of you has a good separate machine for running a dedicated server. If not, many companies can provide a dedicated server for a monthly fee.
  
• reduce the load on the server by reducing the number of (simultaneous) zombies on horde night. This needn’t change the total number of zombies you can get.

It could also be an issue with the data stream on the network. For example, if you're on WiFi, and your router doesn't have a lot of memory dedicated to the WiFi bandwidth, the horde might be enough to overload the data buffer and could cause you a high ping. The could either be on the host side, or on your side.
Similarly it could be caused by security software holding the data packets for scanning. Programs like Norton, McAffee, and EEST are really great at causing issues like this, so we always recommend that you exclude the client.