It is almost like a prose poem at best, and not really parsable as a sentence.
白点 should be simply a white dot referring to the seagull or snowflake (or both even if inconsistent with ひとつ).
One possible interpretation:
曇天に白点ひとつ、さみしく鳴く春かもめが、
Here かもめ is the subject for some missing verb modified by 曇天に白点ひとつ: A spring seagull crying sadly (flies like) a white dot in the cloudy sky.
雪の名残ひとひら、まだ冷たい三月の風だった。
Here both are noun phrases describing the situation: A snowflake (in the air), (there was) March wind which was still cold.
Another possibility is to consider literally かもめが as subject for 三月の風だった: A spring seagull crying sadly, (which looks like) white dot in the cloudy sky, with a snowflake, was the cold March wind.
Anyway it is a description of a scenery with seagull and snow in the cold wind.