There are a few approaches you could use, what works best will depend on what hardware you have and what you want to achieve.
If your only rain gauge is the WS90 then the easiest approach is to alter the Ecowitt Gateway Driver field map to map the WS90 (piezo) rain fields to the standard WeeWX rain fields. This approach requires no change to the Seasons skin (other than perhaps some sensor settings if you wish to display WS90 battery and signal data). You could do as you outlined above and add additional fields to the WeeWX database and alter the Season skin to display these new fields, though if the WS90 is your only rain gauge then that is quite a bit of work for no real benefit. If you have another rain gauge as well as the WS90 then the standard WeeWx rain fields will likely be used by the other rain gauge. In that case you have no choice but to add new fields to the database in which to save the WS90 rain data (and modify the Seasons skin as you indicated). Note that the week, month and year fields are not used by the Seasons skin, so there is no real benefit in adding them to the database. The dayRain field is used by some of the RESTful uploaders, so there may be benefit in providing that field to WeeWX (it must be named dayRain though), but there is no need to add it to the database as only the current value is used.
Assuming the WS90 is your only rain gauge the following field map extensions for the driver should be all that is required, something like:
[GW1000]
....
[[field_map_extensions]]
rain = p_rain
stormRain = p_rainevent
dayRain = p_rainday
weekRain = p_rainweek
monthRain = p_rainmonth
yearRain = p_rainyear
rainRate = p_rainrate
Of the above fields only rain and rainRate will be stored in the database (WeeWX will automatically store data in fields where (1) the field exists in the archive record and (2) the archive table in the database has an identical column name, all other fields are ultimately discarded). This is fine if the Seasons skin is all you are using as the Seasons skin does not use any of the other rain related fields. As mentioned above if you are uploading to WU or PWS then the dayRain field may be of use, though if it is not available WeeWX will calculate the value from the rain field. So unless you have some other need stormRain, weekRain, monthRain and yearRain entries could be omitted without detriment.
Gary