YOU SAID:

Perhaps it was because Natsumi, climbing the stairs, was wearing a jersey, with her hair bundled up into a ponytail, the nape of her neck seemed cool, to the point it chilled me just by looking at it.

INTO JAPANESE

多分それは、階段を登って、なつみは、クールなそれはそれを見るだけで私を冷やしてポイントに見えた彼女の首のうなじポニーテールに束ね髪ジャージーを着ていたためにだった。

BACK INTO ENGLISH

Just maybe it was Natsumi is climbing the stairs, see it is cool but it was cool me and seemed to point her neck's nape of the neck ponytail and wore a Jersey hair.