Because we make a snowman with heaping up a lot of snow,we say it is"堆雪人"dui xue ren."堆"means heaping up.That is to say,put a lot of things together and it looks like a hill.
For example,"The gardener began to heap up the fallen leaves","A little pile of equipment began to heap up on the table".
when we have a snowball fight,we say it is "打雪仗"."打仗da zhang" has several meanings.Sometimes we refer to the wars between armies.For example,we say "德国(Germany)和法国(France)打仗 de guo he fa guo da zhang".That means there is a war between the Germany and the France.Sometimes we refer to the brawling.It usually occurs between several people.
When we have a snowball fight,we throw the snowballs at other people and maybe hit them.It looks like a brawling.But since our "weapons" are snowballs, we use the "雪xue"(snow) to describe the fight.We say it is "打雪仗".
And just like that,if a war between armies is very tough and hard to win,we say it is 打硬仗 da ying zhang。“硬”means hard and tough under the circumstance.
hoping it works.