assuming relatively little interference from traffic, you're only talking about a 15 or 20-minute ride. Take a patch kit or spare tube (or both), tire levers and a pump for sure--I don't go anywhere without those. Throw in a multitool in case something comes loose, but I don't think I've used mine in five or six years (I check the bike over quickly a couple of times a week). You don't specify what you mean by "weather," so it's hard to give specific recommendations. When I lived in California, I used to think 50 degrees was too cold to ride. Here in Reno, I'm often out in the 20s. Just dress in layers and peel as you need to, though in such a short ride you're not likely to overheat. Down to 25-30 degrees, I'm comfortable with a light base layer, even a long-sleeved T shirt sometimes, a windproof shell and whatever the temperature dictates in the middle, from nothing to heavy fleece or wool. Plus gloves, if it's colder than 45 or so.
We don't get much rain here, so riding in it is a treat. Temps in the rain aren't going to be very low, so all you need is something to keep the water off. If you get a lot of it, fenders are a HUGE help.
As long as you shower daily and change your work clothing, smell isn't likely to be a factor. The sweat you generate through exercise has virtually no odor when its fresh. I rode 13 miles to work in street clothes 75-100 days a year for 15 years, and friends (good friends, who'd tell me the truth) said I didn't stink at all. If you overdo the outer garments so you soak your office clothes, I guess that could create problems.
A paper-towel pitwipe in the restroom is helpful, too. Grab a handful, wet half of them at the sink, then duck into the stall, wipe and dry and flush everything down the toilet. A dab of deodorant finishes the job.