On the way I drove backback driving from another county in my city, I saw a car pileup - about six to eight cars bumped togetherwere involved.

The reason for the car accident iwas that the road on the bridge was frozen but, on the normal road, it was not frozen.

But on the normal road, it's not frozen.

This was a sentence fragment so I deleted it and added it to the previous line.

Last night was the first time it snowed where I live.

This sounds like it was the first time it had EVER snowed there. Do you mean the first time this season?

On the way (that) I drove back from another county in my cito my city | On my way home from another county, I saw a car pileup - about six to eight cars bumped together.

This sounds like you witnessed the accident as it occurred. If you came upon it after it had already happened, add “had”: “six to eight cars HAD bumped together.”

If this accident occurred ON a bridge, you could add this information here, too. This would help the reader to understand the subsequent sentence where you mention the bridge.

The reason for the car accident iwas that (the road surface on) the bridge was frozen.

You could omit the part that I put in parenthesis.

But on the normal road, it' was not frozen.

On the way I drove back from another county in my city, I saw a car pileup - about six to eight cars bumped together.

I drove back from another county in my city, and on the way I saw a car pile up, about six to eight cars bumped together.

The reason for the car accident is that the road on the bridge was frozen.

The reason for the car accident was that the road on the bridge was frozen.

But on the normal road, it's not frozen.

On the normal road, it wasn't frozen.