Do legacy nodes receive the witness fields of a Segwit transactions?
Legacy nodes (that is, nodes before segwit) do not receive witness data.

Witness data is a separate data structure. It is only relayed if a node asks for it.

Older nodes don't know it exists, so they don't ask for it, and thus don't receive it.

Since segwit data does not contribute to the txid, old nodes can receive the regular block and still validate it as normal. They just interpret the segwit inputs as "anyone-can-spend" equivalents.