Not sure whether by low-density you mean single-density or double-density, but I'm guessing DD.
To expand on what konc said, the magnetic coating on the disk is slightly different, so the DD drive will have a harder time getting the data to stick on a HD disk - the signal will be weaker.
I've heard the result from this is that the data will become unreadable sooner, but this seems to mean "after 10 years" instead of "after 20 years" so it probably won't be a problem for you. And as long as you have a copy of the data, you can just reformat the disk and copy it back again should you ever run into problems.
The real problem is switching a disk between DD and HD drives. DD drives have 40 tracks, while HD drives have 80 tracks, with each being half the width so it can fit twice as many into the same physical space. This means when a HD drive accesses DD media, it skips every second track so that the 80-track drive mechanism behaves as if there are only 40 tracks. The HD head is of course half the width of the DD head, but it has no problem picking up the DD track even though it's only reading one edge of it.
The problem is if you write data with the HD drive, the head is half the width so you are only writing on the edge of the DD track. If the disk is completely blank (degaussed, unformatted) then this is ok - the DD head will pick up the data from the edge of the track with no other interference. But if there is already data on the disk, then the HD head can only overwrite the edge of the track, leaving the rest of the track untouched, with the original data intact. The DD drive will then see the original track, with different data along one edge, and its wider read head will combine the two signals into one that makes no sense at all, resulting in read errors.
So once a disk has been written in a DD drive, you can no longer reliably write to it in a HD drive because you will never be able to completely update the full-width magnetic signal on the disk surface. Likewise if the HD disk has previously had all 80 tracks written to (by being formatted as 1.2MB) then when you reformat it as 360k in the HD drive, you'll only be writing to the edge of the DD tracks, so the DD drive will see the new and original data at the same time again, causing read errors.
If you format the disks in the DD drive then they will work fine, as the DD head can completely overwrite the full-width tracks. But if you then try to copy data onto the newly formatted disk in the HD drive, you'll be back to the original problem where the data gets written to the edge of the track, so the DD drive will see half the track being formatted and the other half having data on it, and the combined signal will look like nonsense.
So long story short, you can use HD disks in a DD drive, but only in two specific cases. 1) the disk is formatted in the DD drive and only ever used in DD drives, and 2) you use a degaussing wand to completely erase the disk, then use the HD drive to format it in DD mode and write data in the HD drive. You can keep using this disk as long as all writes are done in a HD drive - once you write on the DD drive the disk becomes DD-only and you need to degauss it again before you can write to it in a HD drive.
Sorry if this sounds a bit confusing, it ended up being a bit of a long-winded explanation so I hope it makes sense!