"horse-thing" or "horse-object" seem just too general for me  - they could be anything related to horses. I feel we should involve KHAM/KHAD (English 'saddle' is also derived from a PIE root meaning 'to sit').

Maybe lema "tool to go" or menda "tool to travel"?

I am not sure how -mâ would be attached to MEN (travel).

I'm sorry about those comments. I don't know why they were posted and I am unable to delete them.

Maybe hanwa?

*nortohamma, *roccolannë (cf. Lat. stratum[1]) or similar should be sufficiently interpretable — although poetic language might sometimes call for a shorter word.

Btw: The Romance synonyms come simply from Latin sella "seat, chair; saddle" (and the Ibero-Romance words for "bicycle saddle" are formed with a diminutive suffix from this).

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[1] http://en.wiktionary.org/wiki/stratum#Latin

(Qenya Lexicon appears to contain a 1910's word for "blanket". Note here also Qe alu "dressed leather".)

QL also has sonda "seat" which could be used simply for this purpose. (*roxonda?)

We already have hamma 'chair' (VT45:20). Based on what has been said above, one could simply extend its meaning to be 'chair, saddle'.

What also works is that if there is a root doublet KHAM-/KHAD-, then *khammā and *khadmā start off as synonyms 'seat', but are later differentiated to 'chair' and 'saddle' respectively. (The latter would give *handa or *harma.) This happens all the time, a prominent example being 'sky' vs. 'heaven' in English where the latter has acquired a religious connotation. I somehow suspect that the same happened to Indo-European *sed-l- (or whatever led to 'saddle') as well.