Yes, 肌寒さ is distorting the counts.

肌寒	46502	99.9%
膚寒	42	0.1%

sankoku: はだ寒く感じる＜こと・気温の状態＞

[rare] vs. standard forms:
肌寒い	470861	92.1%
肌寒さ	40400	7.9%

This noun form:
肌寒が	0	0.0% 
肌寒は	0	0.0%
肌寒を	39	0.2%
膚寒が	0	0.0%
膚寒は	0	0.0%
膚寒を	0	0.0%

さ noun form
肌寒さが	4666	19.0%
肌寒さは	2713	11.0%
肌寒さを	17180	69.8%

Here I don't think 肌寒 and 肌寒さ are the same...
肌寒だった	36	6.0%  <-- "it was a chilly day"
肌寒さだった	173	28.9%　 <-- "it was the chilliness of x"
肌寒でした	23	3.8%
肌寒さでした	367	61.3%

「肌寒い」は秋だけ？
https://www.nhk.or.jp/bunken/summary/kotoba/gimon/009.html
Not necessarily, but some may be reluctant to use 肌寒い in the Spring...
「肌寒（はださむ）」は、俳句の秋の季語で、秋が来て肌に空気を冷たく感じることをいいます。したがって、夏の終わりから秋にかけてのころの表現として使うのが伝統的な使い方といえます。「朝夕めっきり肌寒くなりました」春先に「肌寒い」というのは、抵抗感をもつ人もおり、「（少し）ひんやりと・・・」などの言いかえもできます。

book results searching for "肌寒を" vs. "膚寒を" do show the latter as comparatively rare.

This is the standard さ noun form:
https://eow.alc.co.jp/search?q=肌寒さ
肌寒さ
chill（空気などの）〔凍るほどではないが、不快な寒さや冷たさ。〕
chill in the air

I may not be back to see the answer, but has there ever been thought given to marking "seasonal haiku" terms explicitly somehow. Even a parenthetical "(esp. in haiku)", for example, or something like:
chill (seasonal word for "autumn" in haiku); 

I've probably edited a dozen such terms that could be flagged this way, and it would be more informative than [rare]. 

According to sankoku, this doesn't *need* to be an autumn chill, but sankoku *also* says of the adjective 肌寒い: (秋などに)...  

Here's a blog for a fisherman dated mid-summer: 2013年06月16日
https://blog.goo.ne.jp/itizaemon-oncha/e/f316910eb119c8dbab81b6d8d4c57c83
潮は悪かったようだし、朝方は少し肌寒だったし....

JUNE 5, 2022 post about eating icecream on a cold day
https://www.instagram.com/p/Cea1b5Uvc3a/
ちょい肌寒だったけども…新作出たらまずは行かなきゃ

Amazon review in april about deciding to buy a blanket because it was still chilly before summer:
https://www.amazon.co.jp/-/en/gp/customer-reviews/R263A6AL0XT9IQ?ASIN=B091GN76KN
布団が暑いと感じはじめ夏掛けを出して準備をしたが少し肌寒だったので思い切って購入

I think that "chill" = "what the person feels", chilliness = "the state of the weather" (sankoku and daijs both identify these separately, and it somewhat explains the meaning of 朝方は少し肌寒だった)

@@ -8,0 +9 @@
+<ke_inf>&rK;</ke_inf>
@@ -15 +16,3 @@
-<gloss>autumn chill</gloss>
+<misc>&rare;</misc>
+<gloss>chill (esp. in autumn)</gloss>
+<gloss>chilliness</gloss>

koj, daij