Charcoal, 38 bytes

XＦ³²«Ｆ…·±ιιＦ…·±ιι«Ｊκλ›⁼№ＫＭX¹⁼ＫＫX»ＵＭＫＡX

Try it online! Link is to verbose version of code. According to my comment on the Sandbox post I can do this in 37 bytes but unfortunately my computer rebooted to install updates and I didn't save my solution. Explanation:

X

Output the central X.

Ｆ³²«

Grow the snowflake 31 times. (The first loop has no effect since it only checks one square.)

Ｆ…·±ιιＦ…·±ιι«

Check a larger square each time. (This is golfier than hardcoding the size.)

Ｊκλ

Jump to each position in the square.

›⁼№ＫＭX¹⁼ＫＫX

If the cell does not yet have an X but it has one neighbouring X then print a -.

»ＵＭＫＡX

After checking the square, change all the -s to Xs.