I would just keep the halter on him. Maybe take it off at night so he gets used to the on/off process but leave it on for more then 30 seconds.
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No - please do NOT do this as it is VERY dangerous. All it takes is for the halter to "catch" on something in the stall or pasture, or even heaven forbid he scratches his head with a hind hoof and gets hoof caught in halter, for foal to die. Years ago I saw pictures of foals that had gotten halters caught up on things like fencing and they ended up with broken necks.
Instead take foal and dam inside a stall. Give dam hay to keep her busy. Then take a halter into satll and kneel on stall floor. When foal approaches talk quietly to foal, scratch neck as foal gets closer then once foal is fine with your topuching it's neck, nose, shoulder, gently slide nose part of the halter on the foal's neck, all the while talking quietly.
Once that is easily done (do not make the session long but rather 15 minutes or less at least once a day, twice is better) then once you move the nose band of halter over the nose start sliding the crown piece behind foals ears. Suggest you do NOT try to slide over the ears (yet) as that is more threatening.
Now once you can easily halter foal this way then practice sliding halter over the ears.
As far as catching & leading - work on teaching foal that once they are caught they are to stand still then help them relax. Do this by wearing leather gloves and getting a thick cotton rope (NOT nylon - I use a thick cotton lead line about 10 feet long). Start in a larger stall so foal has room to move/walk but not a pasture (too much room). I wrap around foal's neck - and hold both ends in one hand, use other to scratch neck. Once foal is comfortable with than I stand on foals left side, look forward and walk forward - you may want to click at same time.
Foal can either stand still (Pull then release on lead rope), walk forward a step (one is enough more than that great - just do NOT push for too much at once, or leap forward. For the leap forward try to give foal enough room to go forward (you are asking for that) but not keep going (here's where the leather gloves are important to prevent rope burns.
Once foal "leads in the stall then you can try in the pasture. Another trick (in pasture) is having a rop around their butt and using them to encourage them to go forward - but that can be cumbersome, so better to just use the lead line of you can.