|Because of the effects of El Nino, the snowfall was heavy.
The answer is the adverbial “because of.” The “because of” phrase does not modify snowfall. So, it must modify heavy....“heavy because of the effects...” Because “heavy” is an adjective, and adverbs can modify adjectives, you select the adverbial phrase “because of.”
Another way of looking at it that might be easier: The “because of” phrase is giving cause to the “heaviness” of the snow. It's modifying the state of being heavy.
Tip #1: When inclined to use “due to,” move the phrase directly after the connecting verb. If the sentence doesn't read correctly, it's “because of.” Try that with #3: “Due to/because of the effects of El Nino, the snowfall was heavy.” It won't work because the sentence would then read “the snowfall was due to the effects of El Nino heavy.” And that just doesn't make sense.
Tip #2: Whenever you see this “due to/because of” situation at the beginning of a sentence, it's going to be “because of” if a linking verb is involved. Why? Because for “due to” to come into play, the sentence would have to end with the connecting verb because the adjectival “due to” must modify a noun, in this case “snowfall” : “Due to the effects of El Nino, the snowfall was.” And that just sounds funny, to say the least.
The only exception is when referring to the arrival of trains, planes and the like: “Due to arrive a 7:30, the bus was 45 minutes late. It didn't arrive until 8:15.”