so let's check a few basics first... (I dont think this will solve it based on your comments, but lets start here...)
in view, under each connection server, have you configured the SAML Authenticator? and does that point at your horizon gateway?
- on the View Admin Dashboard, the Saml Authenticator health should be showing a Green light.
In Horizon Connector, under the View Pools tab, you should have configured the first connection server. (I am sure this bit is done since you say the desktop icons show in your workspace). However, for each of the connection servers listed, have you Accepted the certificates? and, most importantly, having Accepted the certs, you need to click save to ensure they are saved down to Horizon. If in doubt, please just go back and re-accept those certs and click save again.
Note that you should be able to set SAML as "allowed", which means that launching view should work from the native client directly, AND also from the horizon workspace. Setting to required, means that you can only launch view from horizon workspace.
Further analysis of the problem, then getting a copy of the debug log file from the connection server(s) would be most useful.
cheers
peterB