Remote node signature for HTLC-success and HTLC-timeout transactions
As far as what I have seen, nodes do not exchange their htlcsignatures (although we can derive the htlc public keys through basepoint).


I believe you have overlooked the commitment signed message from bolt 02. From there I quote:


  When a node has changes for the remote commitment, it can apply them, sign the resulting transaction (as defined in BOLT #3), and send a commitment_signed message.


type: 132 (commitment_signed)
data:
[32:channel_id]
[64:signature]
[2:num_htlcs]
[num_htlcs*64:htlc_signature]


While we already see that signatures for all htlcs are transferred we can find the requirements further down :


  A sending node:
  ... 
  MUST include one htlc_signature for every HTLC transaction corresponding to the ordering of the commitment transaction (see BOLT #3).


I believe a node SHOULD NOT  forward the htlc before it validated the signatures from all the htlcs of the received commitment signed.