this is odd, normally "es kam wie es kommen musste" refers to some unpleasant turn of events (..., das Brot fiel auf die belegte Seite.). So "the inevitable happened" is probably not that suitable. In your example, if you are allowed to translate freely, I'd say something like "nature took its due course".

For what it's worth:- It was a fairly long winter and we longed/yearned* for the first rays of the spring sun/of spring sunshine. However spring came as it was bound to come and with its coming it was soon quite warm again.
*yearned is better because you would otherwise have ...a 'long' winter and we 'longed'...