Mine time is displayed by default on the start of the game.

The problem is that scripts, like highlander, override this.

This is more a bug about how to deal with that, I think.

The scripts could be offered the choice to just append to the basic info set, except scripts can mess with a lot of those values, so it could be misleading.

Scripts like highlander should be more responsible and fill out at least some of that info from the game flags.

A lua helper class could assist...

An append option might be more reliable tho.

In the mean time, we should at least try to fix Highlander for next release, given how often it is played.

TL;DR: Just press [Esc] and look on the wind bar at the bottom right of the screen and all your prayers will be heard (note: does not have a 100% success rate)!

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nemo answered this correctly, but incompletely:

Or when you press [Escape] or enter pause mode. This is useful if you forgot the rules of the game, by the way.

However, mine time is not displayed if the mine time is 3 seconds (the default).

This is true as long you play without any scripts (“Normal” style). All scripts with mines should display the mine time, but as nemo said, some fail by doing so, which is lame.
The scripts must be fixed.

This is always displayed at the right bottom of the screen. Also look at the falling objects in most themes (i.e. the coins in Island theme). The float with the wind.
Normally, wind can have any strength from 0% to 100% in both direction, so there is no need for any special message.

If wind is disabled, you'll notice by having 0% wind in every turn. There is no special message for that and I don't think it would be needed.

If the “Wind affects almost everything” mode is enabled, this is also displayed in the [Esc] menu.

EDIT: Argh, crap! Nope, it doesn't. It is impossible to know whether you are in “crazy wind” mode unless it's too late or you're the host. Another bug.

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Now some technical stuff about Highlander and mines:

Fun fact: I made a commit which fixes this, but it got ignored because nemo doesn't like how I commit.

Maybe, just maybe, I clean up my repository one day.

The easy fix would be to just set the Goals variable so the engine strings are kept intact. Normally this should totally be the preferred way if the script does not change many rules.
Highlander should use Goals, because it is simple enough and also allows heavy modification, so we absolutely need the engine strings here (not only mine time, but also stuff like indestructible land, etc.
The annoying thing about Goals is that it can only be set in the beginning of the game and there is no way to change to change “the text after the default message” later, only the full overwrite with ShowMission is then possible.

There is no read access to the default message (listing of GameFlags, basically) at all, so it can not be “faked” either.

I support the idea of the “append” function.

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My final suggestions (for today ):
Questions like “What's the mine time?” get asked extremely often. It seems many newbies don't know they can review the game rules by pressing [Esc]. Maybe, just maybe the [Esc] screen should include an extra line like “Press [Whatever Key] to see this text again”.

Heck, maybe even add a new key binding just for displaying the rules, and you must hold down the key to display the rules. It would be less awkward than having to press [Esc], which actually is for exiting the game anyways.
This function could also be used to force-hide mission texts (by releasing the key) which won't go away on their own (because of long ShowMission timer).

Also, it should be considered to display the mine time of 3 seconds instead of hiding it. I guess only a small select elite knows that “no text in [Esc] screen” means “3 seconds mine time”.
The problem with that might be that it clutters the [Esc] screen with useless info when there are absolutely no mines in the game.

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EDIT: Correction: The “crazy wind” mode is NOT displayed in the [Esc] screen.

WRT. "Wind affects everything" not being displayed. Yeah, we probably should fix that. It's not immediately obvious until you try throwing a grenade or somesuch.

Oh, also, there's kind of a long-standing todo to allow previewing a set of rules in the frontend. That would help too.

The very very simplest would be a large text dump in the alt hover of the scheme dropdown.