My understanding with LTIR is that it only kicks in to give you cap relief when actually up against the cap during the season. So if the Leafs have $70M tied up in contracts, including Horton's, during the season, we are allowed to carry one player whose contract is equal to, or less than, the excess of Horton's contract above the cap. If the Leafs aren't up against the cap, say they're at $60M or so, Horton would still count against the cap because we don't need the space.
So say the cap is $72M, and we have $70M tied up, including Horton (rounded his cap hit to $5M for simplicity), we're allowed to add one roster player whose contract would bring us up to no higher than $75M ($2M in proper cap space, $3M from Horton's LTIR relief).
During the off-season though, there is no LTIR, so all contracts count against the cap, including Horton's. This causes some issue in terms of our wiggle room, but it's important to keep in mind that teams can go an extra 10% above the cap during the off-season. Since that 10% ($7.2M in this example) is more than Horton's contract is worth ($5M), we can still allow ourselves to build our full roster in the off-season, as long as we don't try and get too cute taking on other teams' dead weight. So it restricts what we can do as a middle-man or facilitator, but should have very little effect on how we properly conduct our actual team-building.
With regards to Stamkos, this would mean we would only need the difference between his new contract and Horton's contract in actual free cap space at any time. So if we sign Stammer for $10M, we need $5M in cap space, as the 10% offseason overage, and Horton's in-season LTIR, should allow for the rest. Obviously Stamkos' contract can't be used as Horton's replacement, since it's twice the cost, but we wouldn't look at it that way anyway, we'd have someone else as Horton's relief player.
That's my understanding anyway. I'm no capologist, so someone can feel free to let me know if I'm wrong.