It was snowing heavily until now but, it's dying down
さっきまでは様々な言い方がありますが分かりやすい
until now と言う表現が良いと思います。
雪が強く降っていたは英語では重く降ると言う感じで
It was snowing heavily と言います。
弱くなってきたは徐々に強くなくなるとの意味で
dying down と言う表現を使うと良いです。
Up until a few moments ago it was snowing very heavily but it isn't anymore
It was snowing heavily up until a few moments ago but now it's quite light
「さっきまで雪強く降ってたけど、弱くなってきた」は英語で Up until a few moments ago it was snowing very heavily but it isn't anymore. もしくは It was snowing heavily up until a few moments ago but now it's quite light. になります。
強い= strong、弱い= weak なのですが雪の場合は strong snow や weak snowは言いません。Heavy もしくは light snow と言います。
さっきまで - up until a few moments ago.
雪 - snow
強く降ってた- was falling heavily
けど - but
弱くなっている - got weak
Heavy snow we had until thirty minutes ago started to abate.
heavy snow =「強い雪」
heavy snow we had until thirty minutes「30分前まで降っていた雪」
abate＝「（勢いなどが）弱まる」
started to abate＝「弱まり始めた」
Heavy snow we had until thirty minutes ago started to abate.
「30分前まで降っていた強い雪が弱まり始めた」
ご参考まで
日本 
イギリス 
