To add a little more confusion into the calendrical mix I've just been browsing the fount of all knowledge, Dwelly, and he tells us that the months could be held back depending on the weather. So March wouldn't start until the weather was good for agricultural purposes. They even have old sayings for this sort of thing.
'Màrt -àirt, sm Month of March. 2 Tuesday. 3 Time suitable for agricultural work. 4* Busiest time at anything. 5 Great haste. 6* Seed-time.
There appears to be considerable confusion in Gaelic proverbs etc regarding the first three significations given above for Màrt, as is exemplified in the following notes from Nicolson's Gaelic Proverbs (NGP), Waifs & Strays (W) and Carmina Gadelica (AC).
In the first place the old “months” appear to have been moveable and depended for the time of their commencement upon whether the suitable weather had already arrived. If the weather had not come, neither had the month, e.g. Luath no mall g' an dig am Màigh, thig a' chuthag, late or early as May comes, (i.e. as May weather comes), so comes the cuckoo. The Names of several months or rather periods of various lengths occur twice, while Màrt occurs no less than three times.
The comparatively modern Màrt O.S., which is still in vogue in some parts, (says AC in speaking of the months in general) being still used in an O.S. manner, does not commence until the orthodox calendar month is half gone. AC i. 245, ii. 263 & NGP 413, both make Màrt extend into April. Nicolson appears to have been puzzled, for his explanations are obscure. On p. 26 (NGP) he translates “an ciad Mhàrt” as the first Tuesday, while from a note explaining the same proverb, it is evident that he thought Màrt stood for March.
The first Tuesday of the sowing-time or times, would appear to be “an ciad Mhàrt de Mhàrt na curachd,” in the same way as there was a Bealltainn of the Bealtainn and a Lùnastal of Lùnastal. AC gives “gaoth gheur nam Màrt” (pl). NGP p. 26 speaks of three Màrts. W. iii. 218, 298, 299 speaks of three — Apr. 12 to May 1, Aug. 12, Sept. 12 — (This triple occurrence of 12 is noteworthy).
NGP says 1st week of April is too soon to sow, so he would appear to prefer the 2nd or 3rd week. Is fhearr an sneachd na 'bhith gun sian, an déidh an sìol a chur san talamh, better snow than no rain-storm, when the seed is in the ground, (p. 251) shows that sowing were better done when snow is out of season, i.e. late in April. AC says seed is winnowed by “gaoth gheur nam Màrt,” before being sown, therefore the Màrt or Màrts must be nearly over, i.e late in April, before the seed is in the ground. W. gives Apr. 12 to May 1, i.e. late in April. Another proverb, (NGP. 24) Am feur a thig a-mach sa Mhàrt, théid e staigh sa Ghiblean, the grass that comes out in March shrinks away in April, implies that seed should not appear till Màrt be over or else it will he killed by the weather.
On the other hand, NGP gives Is fhearr aon oidhche Mhàirt na trì latha Foghair (for growth), so the seed, to judge by this, ought to be coming up in March, or else that sowing ought to be done earlier. [It is most likely that it is not growth which is referred to in this proverb, as Nicolson supposes, but the winnowing referred to by AC]. NGP says Tuesday for sowing, AC prefers Friday. There was also the “fìor” or suitable Màrt.'
http://dwelly.info/We are always told that March is named after the Roman god of war but perhaps it's named after the local cattle market. I'm sure that would make more sense to people more interested in where their food is coming from than what Roman gods were getting up to.