A freezethrower centered DM map is a good concept.
IIRC the "no weapon start" Death Row sector tag only works the first time you start the map. Any respawn after that in DM or Co-op and you will start with the pistol.
It may even only work the first time only for player 1 but I could be remembering that wrong. If it is the case I'd just get rid of the tag altogether to avoid disadvantage at the start of the map.
Even then the map should remain fun and as long as there is no pistol ammo around and the gimmick should remain. Actually it may be even more fun with some pistol ammo, half of the fun with frozen opponents is stealing somebody else's kill.
Funny thing is that Redneck Rampage has a similar glitch in Nut House. If you die you'll restart the map with the pistol.
Edit: had a look at the map and it looks good but if I may I have some suggestions.
There is only 2 spawn points so it's only for 1vs1 so my comment about stealing kills can't apply. I'd recommend adding a couple more spawn points even if the map is still intended for 1v1: with only 2 spawn points players have a 50% chance to guess where the opponent will spawn. In such a small map it can quickly get aggravating and lead to successive direct kills at spawn, with camping too, which can potentially get even worse since the spawn points are dead ends, with only the starting pistol too, while the opponent does have access to freezethrower ammo AND health just next to the dead end's exits. You really have to be careful with dead ends and spawn points in DM.
Another potential fix is to hand out the freezethrower directly in the spawn room but I suppose having to run around un-armed for a couple of seconds is intended; and even though it wouldn't fix it completely as when you spawn, your opponent did earn an atomic health from your death, giving him the advantage.
Besides, freezethrower gameplay is a lot more fun with 3-4 players, like I said stolen kills are fun, so a couple more spawn points can't hurt.
The see through wall/forcefield in the middle is a good idea, but it'd be even better if walls in the side corridors allowed for precise freeze projectile bouncing. This can easily be achieved by making those small 45° walls longers, the ones on the side corridors. On grid 1 they're 1 square long, try 3 squares and witness the magic unfold as you can see your opponent through the forcefield and make the projectiles bounce to him. Perhaps a couple of those walls could be mirrors, too.
As a consequence I'd also give a smaller repeat to the forcefield so it's easier to aim using the 45° walls and see what you're doing.
Freeze projectile bouncing is very underrated so more/bigger 45° walls as a while could really make it insane.
It's good that you included an atomic health, it evens things up since frozen kills hand them out, moreover it's placed in a very risky spot. This being said, if you stand around the small 45° walls and look at both the forcefield and the vent you'll see HOM which can easily be fixed by cutting the vent into 3 just before where the forcefield is located rather than 'in' the forcefield's location.
Also at the moment, you can see whether or not the atomic health has respawned before even entering the vent. By hiding it behind a small niched corner, the risk/reward factor would be increased ten folds. Again, 45° walls cornering that niche would guarantee a less safe return if you see your opponent on one side.
A bit less important but if it was me I'd also put the boxes with supplies on them further apart. Force the player to jump a little and take risks. Imagine jumping from a high box to another, on your way to a health pack, get frozen by opponent in the middle of it, and fall to your death as your frozen state breaks apart on the ground and it counts as a suicide. It should be a rare situation, but an amazing one when it happens. Take advantage of everything the freezethrower has to offer. In one of my DM maps I had an atomic health placed on a box which required a near pixel perfect strafe-running jump, and
it lead to some amazing things.
Hope I don't sound like a dick. I just realized I miss DukeMatch.