There is a strong relationship between a person's body being cold and other illnesses.
The connection between being sensitive to the cold and suffering from other illnesses is very relevant.
どちらも「冷えと他の病気との関連性は大いにある。」というニュアンスです。
この場合、relationship to は使えませんせが、relationship between を使えばなんとか言えるかな、と思います。
1) There is a strong relationship between a person's body being cold and other illnesses.
There is a strong relationship between ... and ... で「…と…の関連性は大いにある」
2) The connection between being sensitive to the cold and suffering from other illnesses is very relevant.
... and ... is very relevant で「…と…は大いに関連している」
ご参考になれば幸いです！
日本 
