Users can customise symbology using WFS in ArcMap,
but not WMS.
WMS is essentially an image of the data so the styling is defined, as provided by the data custodian, within the service. For example:
The instructions for customising symbology
using WFS in ArcMap are outlined below:
Add WFS services. See the How to Guide for the steps to add WFS.
Double click on the required layer in the table of contents to open the 'Layer Properties'. Then follow the ESRI guides on styling data using desktop ArcGIS:
Customising symbology using WMS in QGIS
Users can restyle WMS data in QGIS, however the functionality is limited to rendering and resampling: