I had my tires changed to snow tires last December, but it rarely snows or settles, nor does the snow pile up on the ground inear my place.

It’s not that it never snows and sticksor that the snow never piles up.

Sometimes the snow piles up about once a year, but Iin these past few years, I don't think ithe snowed and stuck has piled up that high.

I’m scared of snowy roads.

or: "...snowy road conditions."

One of the my friends told me that “Even with snow tires, the car iscan slip”.

Snow tTires

Sometimes the snow piles up about once a year, but Iin these past few years, I don't think it snowed and stuck.

I’m scared of snowy roads.

One of the my friends told me that “Even with snow tires, the car iscan slip”.

Snow tTires

Title case is generally required for titles, but not always. Especially for casual journal entries like this I usually only capitalize the first word, as you have done here but I just wanted to point it out.

I had my tires changed to snow tires last December, but it rarely snows or settles on the ground inaround my place.

around my place というのは家の周りことです。例えば近所とか。

Sometimes the snowThe snow usually piles up about once a year, but Iin these past few years, I don't think it has snowed and stuck.

Your sentence is grammatically correct but I've just provided a slightly more natural alternative.

"Sometimes" and "About once a year" have a very slight contradiction in the nuance
sometimes: irregular/unpredictable occurrence
about once a year: fairly regular occurrence

I’m scared of snowy roads.

One of the my friends told me that “Even with snow tires, the car iscan slip”.

I had my tires changed to snow tires last December, but it rarely snows or settles on the ground in my placewhere I live, and when it does snow it rarely sticks.

Sometimes tThe snow piles up about once a year, but Iin these past few years, I don't think it has snowed and stuck.

I’m scared of snowy roads.

One of the my friends told me that, “Even with snow tires, theyour car iscan slip”."

That's right, that's right…true...

In English we really only need to say it once. But I understand that in Japanese people often say ”そうそうそう” :)

I had my tires changed to snow tires last December, but itsnow rarely snows or settles on the ground in my placaccumulates where I live.

Snowing is one thing, and accumulating, which is what Google Translates matches with your Japanese, is another; since it has to snow to accumulate, I don't think you need both verbs. "Piles up" is another way to say accumulates.

It’s not that itsnow never snows and stickaccumulates.

Your sentence is fine. "Sticking" is a common way to talk about what snow does when it stays on surfaces for a while.
I'm just showing how you could continue with accumulates if you chose to.

[Sometimes the snow piles up about once a year], but Iin these past few years, I don't think it has snowed and stuck.

"Sometimes" and "about" and "once a year" all in a row makes the statement vague and possibly confusing. It's better to be clear about which it is and use just one of these.

I’m scared of snowy roads.

One of the my friends told me that, “Even with snow tires, the car iswill still slip”.

"will still slide" is what Google Translate gave me. If you are quoting directly, you use a comma and quotation marks.
If you are reporting speech indirectly, you use "that."

One of the my friends told me that even with snow tires, the car will still slip.

That's right, that's right…

Although there are no errors, it seems incomplete to end this way. A stronger closing would be more definite and end with a period:
That's true.
I agree.
I know.

Snow tTires

I had my tires changed to snow tires last December, but it rarely snows or settles on the ground inat my place.

It’s not that it never snows and stickssnow never piles up.

I think using "pile up" here sounds better than snow sticking.

Sometimes the snow piles up about once a year, but Iin these past few years, I don't think it snowed and stuckhas.

I’m scared of snowy roads.

One of the my friends told me that “Even with snow tires, the car iscan slip”.

That's right, that's right…

The sentence is correct. Depending on how you meant it, another option could be "I know, I know...". This option works if you meant this sentence in a weary way.