Which interface of ASA B are you trying to ping? I assume the inside interface and it is the interface subnet that is part of the crypto ACL? If that is the case, have you configured "management-access inside" command on ASA B, that will allow you to ping the ASA B inside interface from ASA A LAN.
When you define the snmp server ip address on ASA B, you would need to configure the "inside" interface so it is sourced from the inside interface which again I assume is part of the crypto ACL interesting traffic for the VPN.