Can I weather target at the ad level?
The weather targeting for AdWords works at the campaign level (or, more specifically at the geo level), rather than at the ad group level in AdWords, and at the Ad Set level for Facebook & Instagram.
This is due to the specific way that AdWords and Facebook handle geo breakdowns - in AdWords its at the campaign level and in Facebook its at the ad set level.
Therefor it is not possible to trigger ads at the ad level in either platform, however there is an easy workaround to this...
Workaround - how to sync your ads with weather
If you are looking to set up ad-specific triggering, you would simply create 2 or more campaigns in AdWords (or 2 or more ad sets in Facebook).
For example, campaign 1 would be your 'snowy campaign', with your 'snowy' ad. Campaign 2 would be your 'sunny campaign', replete with the 'sunny' ad. You could even have a 3rd campaign with a generic ad, which would be triggered when the weather wasn't snowy or sunny. This would ensure that at least one of your ads was always showing.
Your geo targets, would be the same across all 3 campaigns, but you may allocate more budget to the generic campaign, depending on the markets you were targeting, as this might be the one getting the most impressions (most commonly occurring condition).
You would then import all campaigns into WeatherAds, and then applying the corresponding weather targeting to each - sunny trigger to campaign 1, snowy trigger to campaign 2, and the reverse trigger ('NOT snowy or sunny') to campaign 3.
This setup would ensure that the 3 ads would never be running simultaneously - as the rules are all mutually exclusive.