first of all SNMP package is optional, if you want to install that package then you need to install it on all the nodes.
By using SNMP trap all nodes collect information and all UI statistics which will work using SNMP component.
one more important note: while you are configuring multi zimbra, you need to setup single SNMP broadcast ID. by default it will set your fully qualified host name that you need to change while you setup
+SNMP Trap hostname: yourdomain.com
SNMP trap hostname need to be unique for all instances.