I have been trying to compile a list of the names of early-flowering snowdrops. By 'early' let's say pre-Xmas (in my locale) or at-the-same-time-as or before 'Three Ships' anywhere. For simplicity, I have excluded named cultivars from those species that only flower early, which are:
reginae-olgae (ssp. reginae-olgae) [syn. corcyrensis - meaning from Corfu but frequently also applied more widely]
peshmenii
cilicicus
snogerupii
because you can tell just from the species that the plant is early flowering.
What I'm left with is a list of names, the majority of which are G. elwesii. In a few cases I could not identify the species so if they turn out to be reginae-olgae I will take them off the list. I'm open to suggestions of other names or help with identifying unknown species.
'Advent' - elwesii var. elwesii (two separate marks).
'Armistice Day' - elwesii var. monostictus (Rare - I only know of one person who still grows this).
'Athenae' - elwesii var. monostictus
'Autumn Beauty' (& 'Autumn Belle') - possible elwesii / reginae-olgae hybrid.
Pictures (I think of 'Autumn Belle') and
more details‘Budenzauber’ ?? Hagen’s'Barnes' - elwesii var. monostictus
'Blue Octopus' elwesii var. monostictus with long leaves, distributed by Matt Bishop.
from Broadeigh Gardens - elwesii cited in The Garden October 2015 p66.
'Castlegar' - hybrid? Small inner mark, possibly two scapes
'Christmas Cheer' Rare hybrid bred in the USA. See comment from Chris Sanham.'Donald Sims' Early' - elwesii var. monostictus, originally distributed by Rod Leeds.
‘Dorothy Foreman’ elwesii var. monostictus with "shallow 'horizontal' outer segments" and green leaves distributed by North Green Snowdrops.
'Earliest' - by no means the earliest. Elwesii var. monostictus , rare but perhaps one to be consigned to history?
'Earliest of All' - possibly a synonym of 'Barnes'.
'Early to Rize' - hybrid, part rizhensis distributed by North green Snowdrops
'Else Grollenberg' elwesii var. monostictus (distinctively long outer petals, sometimes with green tips). From Wim Postema, large bulbs.
Pictured on the originator's web site and
on the forum.'Emmelina' elwesii var. monostictus (Very early. Named and distributed {thus far only sparsely} by Steve Owen).'Faringdon Double' elwesii-like with three outers and ~six inners
'Frank Lebsa' elwesii with large green marks at the apex of the outer petals and covering about 1/3 of the petal length.
Picture from Ruben Billiet.
'Frinton Advent' - elwesii var. elwesii (similar to 'Advent', possibly later)
'Frühes Elegantes' - elwesii var. monostictus with heart-shaped mark on inners, long outers with green tips. November flowering, named by Clemens Heidger.
'Gabriel' - elwesii var. monostictus (possibly only recognisable if you bring it indoors)
'Haconby Early' - elwesii var. monostictus distributed by Cliff Curtis
'Grüne Weinacht' elwesii, virescent, (an example of several of Hagens still 'in the pipeline')'Hoggets Narrow' elwesii var. elwesii, December flowering distributed by Matt Bishop
'Hoggets Round' elwesii var. elwesii, another December flowering distributed by Matt Bishop
'Hollis' - elwesii var. monostictus (large leaves - from Dr Dowling Munro).
'Howard Wheeler' - elwesii var. monostictus (darker green mark and ovary than in the norm)
'J. Haydn' - elwesii (distinguishing features not known).
‘Kinn Macintosh’ – elwesii (var elwesii with a generous single mark). Distributed by Bob Brown of Cotswold Garden Flowers
'Kryptonite' - elwesii with large strong green marks on apical half of the outer petals. Possibly not consistently early.
Picture here'Lady Latife' - rizehensis "Chunky rounded flowers, often with 2-3 scapes per bulb. Vigorous. Mid-green leaves. Oct-Dec. Ht 20 cm." A new introduction from Paul Barney's Edulis Nursery.
'Manor Farm Early' - elwesii (similar to Remember Remember?) ex Gill Richardson
'Mary Hely-Hutchinson' – plicatus (earliest known plicatus?).
Picture here.'Midwinter' - elwesii.
'Mrs Macnamara' nivalis x elwesii
'November Snow' - transcaucasicus
'Peter Gatehouse' - elwesii var. elwesii
'Potter's Prelude' - elwesii var. monostictus (distributed by Carolyn Walker in the USA)'Rainbow Farm Early' - elwesii var. monostictus originating from Michael Broadhurst
'Remember Remember' - elwesii var. monostictus (quite tall)
‘Santa Claus’ Hybrid? (ex Timothy Clark)
'Smaragdsplitter' elwesii with a solid green mark on the outer petals
Picture here‘Sweetheart’ elwesii (large, very flat outers with a variable green patch, sweet violet scented, ex Michael Broadhurst).
Picture from Ruben Billiet here.'Sheds and Outhouses' ?? green tips on outer petals
'Standing Tall' elwesii var. elwesii with joined marks (tall elwesii, new from the USA, Pictured on Carolyn Walker's web site ). 'Three Ships' plicatus (supposedly in flower 'on Xmas day in the morning')
Tanscaucasicus early form added to the list because Wol & Sue Staines were selling this in 2017 (see also 'November Snow')
'Xmas' elwesii with an x-shaped mark on the inner petals, another snowdrop from Carolyn Walker in the USA.'York Minster' elwesii, virescent (new, like an early-flowering version of 'Rosemary Burnham', possibly not consistently early, ex Jörg Lebsa)
'Yuletide' elwesii.
Hagen tells us there are (mostly unnamed?) groups of G. rizehensis and G. transcaucasicus which flower early. There was a recent report of an autumn-flowering form of G. plicatus (var. byzantinus).
I'm editing this list as we go so references to corrections and omissions in the comments below should become incorporated into this first post.
Michael Myers has compiled a similar but more wide-ranging list of early-flowering snowdrops. This is attached to
this forum post. I was unaware of several of the snowdrops on this list until I read the one compiled by Michael
Snowdrops shown in blue are from the USA and are not necessarily available in Europe.Snowdrops shown in orange have been mentioned on this Forum but are new ones which I know are not yet commercially available. 
