I know that there are shrines that have a frostblades in chests. I also know that there is one in a labyrinth and in the Coliseum. Except I don't have the Coliseum unlocked. So is there a mini boss/monster somewhere that drops the frostblade?
The Coliseum is the best place to get elemental weapons, and you don't need to unlock it as you seem to think. I've included a picture from this interactive map: https://www.zeldadungeon.net/breath-of-the-wild-interactive-map/ You can see the Coliseum ruins near the middle of the map (marked by the bow and arrow icon). The Great Plateau is near the bottom middle as a reference point, and the stable shown on the left/top part is the Outskirt Stable. Just go into that Coliseum and have at it.
Warning about entering that area:
There is a Lynel at the bottom. If you aren't prepared to fight it, I recommend not using the front door (north side). Climb up over the walls or mountain, and enter from the top. There are 3 floors above the Lynel. Each floor contains enemies with frost, lightning, and fire weapons respectively.
There are a couple alternatives to find that weapon apart from the Coliseum.
- Rewards in two other shrines: Jitan Sa'mi Shrine and Namika Ozz shrine.
- They are carried by Lizalfos on some places but a particular spot is in the Hebra region, one of those big skull camps with monsters. one of the Lizalfos carries one (As shown in the map below)
Note: Haven't included intentionally any spoilers such as the location of the Shrines or any additional information on the map.
The image was edited from this original source. https://i.ytimg.com/vi/DLT1ELm0Irg/maxresdefault.jpg