yes, you can set output cache for webform pages. you can do it through web.config. it looks like below

<caching>
<outputCacheSettings>
<outputCacheProfiles>
<add name="xxx" enabled="false" duration="3600" varyByParam="*" varyByContentEncoding="gzip;deflate" />
</outputCacheProfiles>
</outputCacheSettings>
</caching>

Thanks @Duke! did you mean to set Enabled to true though? This is what we currently have:

<caching>
<outputCacheSettings>
<outputCacheProfiles>
<add name="ClientResourceCache" enabled="true" duration="3600" varyByParam="*" varyByContentEncoding="gzip;deflate" />
</outputCacheProfiles>
</outputCacheSettings>
</caching>

However it is not working and despite many attemps we cannot figure out why. 

If you have been able to make it work in the past, then at least we know it's possible. 

yes, I mean to set Enabled to true. May I know how do you realize that the output cache does not work?

Try setting the key "httpCacheExpiration" to something like "01:00:00" in the tag <episerver> like this:

<episerver>
    <applicationSettings httpCacheExpiration="01:00:00" httpCacheability="Public" />
</episerver>

This enables the output cache in Episerver.